Number of the day: 571682

Properties of the number 571682:

571682 = 2 × 285841 is semiprime and squarefree.
571682 has 2 distinct prime factors, 4 divisors, 21 antidivisors and 285840 totatives.
571682 has a prime digit sum 29 in base 10.
571682 = 401² + 641² is the sum of 2 positive squares in 1 way.
571682 = 19² + 36² + 755² is the sum of 3 positive squares.
571682² = 250080² + 514082² is the sum of 2 positive squares in 1 way.
571682² is the sum of 3 positive squares.
571682 is a proper divisor of 277¹⁸ - 1.
571682 is an emirpimes in (at least) the following bases: 2, 6, 8, 11, 13, 15, 23, 24, 25, 28, 34, 43, 44, 54, 55, 61, 63, 64, 65, 66, 69, 80, 82, 84, 91, 95, 96, and 99.
571682 is palindromic in (at least) base -97.

Number of the day: 32139

Properties of the number 32139:

32139 = 3² × 3571 is the 28691^th composite number and is not squarefree.
32139 has 2 distinct prime factors, 6 divisors, 11 antidivisors and 21420 totatives.
32139 = 16070² - 16069² = 5358² - 5355² = 1790² - 1781² is the difference of 2 nonnegative squares in 3 ways.
32139 is the difference of 2 positive pentagonal numbers in 1 way.
32139 = 17² + 35² + 175² is the sum of 3 positive squares.
32139² is the sum of 3 positive squares.
32139 is a proper divisor of 103³ - 1.
32139 = '321' + '39' is the concatenation of 2 emirpimes.
32139 is palindromic in (at least) the following bases: 37, -33, -43, and -63.
32139 in base 34 = rr9 and consists of only the digits '9' and 'r'.
32139 in base 37 = NHN and consists of only the digits 'H' and 'N'.
32139 in base 42 = I99 and consists of only the digits '9' and 'I'.

The number 32139 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004932: Floor of n*phi^17, where phi is the golden ratio, A001622.
A004952: Nearest integer to n*phi^17, where phi is the golden ratio, A001622.
A114613: Starting numbers for which the RATS sequence has eventual period 3.
A224749: Vauban's sequence: a(n)=0 if n<=0, a(1)=1; thereafter a(n) = 3*a(n-1) + 6*a(n-2) + 6*a(n-3) + 6*a(n-4) + 6*a(n-5).
A251310: Number of (n+1) X (1+1) 0..1 arrays with no 2 X 2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements.
A288492: Indices of terms of A288349 that are powers of 2.

Number of the day: 294229

Properties of the number 294229:

294229 = 13² × 1741 is the 268676^th composite number and is not squarefree.
294229 has 2 distinct prime factors, 6 divisors, 13 antidivisors and 271440 totatives.
294229 has a triangular digit sum 28 in base 10.
294229 = 147115² - 147114² = 11323² - 11310² = 955² - 786² is the difference of 2 nonnegative squares in 3 ways.
294229 is the difference of 2 positive pentagonal numbers in 3 ways.
294229 = 215² + 498² = 198² + 505² = 377² + 390² is the sum of 2 positive squares in 3 ways.
294229 = 105² + 152² + 510² is the sum of 3 positive squares.
294229² = 113165² + 271596² = 103896² + 275275² = 122304² + 267605² = 9971² + 294060² = 207179² + 208920² = 199980² + 215821² = 201779² + 214140² is the sum of 2 positive squares in 7 ways.
294229² is the sum of 3 positive squares.
294229 is a proper divisor of 59¹⁵⁶ - 1.
294229 = '2' + '94229' is the concatenation of 2 prime numbers.
294229 is palindromic in (at least) base 100.

Number of the day: 1087

Properties of the number 1087:

1087 is a cyclic number.
1087 is the 181^th prime.
1087 has 13 antidivisors and 1086 totatives.
Reversing the decimal digits of 1087 results in a semiprime.
1087 = 544² - 543² is the difference of 2 nonnegative squares in 1 way.
1087 is the sum of 2 positive triangular numbers.
1087 is the difference of 2 positive pentagonal numbers in 1 way.
1087 is not the sum of 3 positive squares.
1087² is the sum of 3 positive squares.
1087 is a proper divisor of 257³ - 1.
1087 = '10' + '87' is the concatenation of 2 semiprime numbers.
1087 is an emirp in (at least) the following bases: 2, 6, 13, 14, 15, 17, 19, 21, 25, 28, 29, 30, 34, 35, 37, 40, 41, 42, 43, 49, 50, 53, 56, 59, 61, 62, 67, 73, 75, 81, 83, 92, 94, 95, 97, and 99.
1087 is palindromic in (at least) the following bases: 12, -11, and -31.
1087 in base 12 = 767 and consists of only the digits '6' and '7'.
1087 in base 32 = 11v and consists of only the digits '1' and 'v'.

The number 1087 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006450: Prime-indexed primes: primes with prime subscripts.
A007522: Primes of the form 8n+7, that is, primes congruent to -1 mod 8.
A008483: Number of partitions of n into parts >= 3.
A008865: a(n) = n^2 - 2.
A022005: Initial members of prime triples (p, p+4, p+6).
A023200: Primes p such that p + 4 is also prime.
A107132: Primes of the form 2x^2 + 13y^2.
A139643: Primes of the form x^2+Ny^2, with N=102.
A140633: Primes of the form 7x^2+4xy+52y^2.
A235482: Primes whose base-5 representation is also the base-9 representation of a prime.

Number of the day: 651

Properties of the number 651:

651 = 3 × 7 × 31 is a sphenic number and squarefree.
651 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 360 totatives.
651 has an oblong digit sum 12 in base 10.
651 has a sphenic digit product 30 in base 10.
651 has an oblong digit product 30 in base 10.
Reversing the decimal digits of 651 results in an oblong number.
651 = (10 × 11)/2 + … + (16 × 17)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
651 = 326² - 325² = 110² - 107² = 50² - 43² = 26² - 5² is the difference of 2 nonnegative squares in 4 ways.
651 is the sum of 2 positive triangular numbers.
651 is the difference of 2 positive pentagonal numbers in 1 way.
651 is the difference of 2 positive pentagonal pyramidal numbers in 1 way.
651 = (21 × (3 × 21-1))/2 is a pentagonal number.
651 = 1² + 5² + 25² is the sum of 3 positive squares.
651² is the sum of 3 positive squares.
651 is a proper divisor of 433² - 1.
651 = '6' + '51' is the concatenation of 2 semiprime numbers.
651 is palindromic in (at least) the following bases: 5, 6, 25, 30, 92, -4, -5, -26, -50, and -65.
651 in base 5 = 10101 and consists of only the digits '0' and '1'.
651 in base 6 = 3003 and consists of only the digits '0' and '3'.
651 in base 24 = 133 and consists of only the digits '1' and '3'.
651 in base 25 = 111 and consists of only the digit '1'.

The number 651 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000326: Pentagonal numbers: a(n) = n*(3*n-1)/2.
A001106: 9-gonal (or enneagonal or nonagonal) numbers: a(n) = n*(7*n-5)/2.
A001157: sigma_2(n): sum of squares of divisors of n.
A001318: Generalized pentagonal numbers: m*(3*m - 1)/2, m = 0, +-1, +-2, +-3, ....
A002061: Central polygonal numbers: a(n) = n^2 - n + 1.
A005728: Number of fractions in Farey series of order n.
A006095: Gaussian binomial coefficient [n,2] for q=2.
A022166: Triangle of Gaussian binomial coefficients (or q-binomial coefficients) [n,k] for q = 2.
A027441: a(n) = (n^4 + n)/2, (Row sums of an n X n X n magic cube, when it exists).
A139250: Toothpick sequence (see Comments lines for definition).

Number of the day: 6593

Christiaan Huygens was born on this day 392 years ago.

Properties of the number 6593:

6593 is a cyclic number.
6593 = 19 × 347 is semiprime and squarefree.
6593 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 6228 totatives.
6593 has a prime digit sum 23 in base 10.
6593 = 3297² - 3296² = 183² - 164² is the difference of 2 nonnegative squares in 2 ways.
6593 is the difference of 2 positive pentagonal numbers in 2 ways.
6593 = 7² + 12² + 80² is the sum of 3 positive squares.
6593² is the sum of 3 positive squares.
6593 is a proper divisor of 229¹⁷³ - 1.
6593 = '659' + '3' is the concatenation of 2 prime numbers.
6593 = '65' + '93' is the concatenation of 2 semiprime numbers.
6593 is an emirpimes in (at least) the following bases: 3, 4, 8, 9, 16, 21, 26, 29, 30, 31, 32, 34, 37, 51, 54, 55, 57, 61, 62, 68, 71, 72, 78, 80, 87, 89, 95, and 100.
6593 is palindromic in (at least) the following bases: 6, 36, 64, and -6.
6593 in base 22 = ddf and consists of only the digits 'd' and 'f'.
6593 in base 35 = 5dd and consists of only the digits '5' and 'd'.
6593 in base 36 = 535 and consists of only the digits '3' and '5'.
6593 in base 40 = 44X and consists of only the digits '4' and 'X'.

The number 6593 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A039515: Conjecturally, largest attractor in '3x+(2n+1)' problem.
A047986: Integers n such that A047988(n)=3.
A062725: Write 0,1,2,3,4,... in a triangular spiral, then a(n) is the sequence found by reading the terms along the line from 0 in the direction 0,7,...
A068059: Partial sums of A068058 + 1.
A073592: Euler transform of negative integers.
A074340: a(1) = 5; a(n) is smallest number > a(n-1) such that the juxtaposition a(1)a(2)...a(n) is a prime.
A100294: Numbers of the form a^5 + b^4 with a, b > 0.
A105728: Triangle read by rows: T(n,1) = 1, T(n,n) = n and for 1 < k < n: T(n,k) = T(n-1,k-1) + 2*T(n-1,k).
A238553: Numbers n such that the decimal expansions of both n and n^2 have 3 as the digit with the smallest value and 9 as the digit with the largest value.
A246325: Total number of ON cells at stage 2n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by "Rule 453".

Number of the day: 8009

Kari Onni Uolevi Karhunen was born on this day 106 years ago.

Properties of the number 8009:

8009 is a cyclic number.
8009 and 8011 form a twin prime pair.
8009 has 9 antidivisors and 8008 totatives.
8009 has an emirp digit sum 17 in base 10.
8009 has sum of divisors equal to 8010 which is an oblong number.
8009 = 1³ + 2³ + 20³ is the sum of 3 positive cubes in 1 way.
8009 = 4005² - 4004² is the difference of 2 nonnegative squares in 1 way.
8009 is the difference of 2 positive pentagonal numbers in 1 way.
8009 = 28² + 85² is the sum of 2 positive squares in 1 way.
8009 = 17² + 18² + 86² is the sum of 3 positive squares.
8009² = 4760² + 6441² is the sum of 2 positive squares in 1 way.
8009² is the sum of 3 positive squares.
8009 is a proper divisor of 283⁴ - 1.
8009 is an emirp in (at least) the following bases: 2, 4, 11, 18, 23, 26, 29, 31, 35, 38, 41, 46, 49, 50, 63, 65, 67, 71, 76, 81, 84, 85, 87, 89, 91, 92, 93, 94, 96, 97, and 98.
8009 is palindromic in (at least) the following bases: 77, 88, and -91.
8009 in base 36 = 66h and consists of only the digits '6' and 'h'.

The number 8009 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A002327: Primes of form n^2 - n - 1.
A033274: Primes that do not contain any other prime as a proper substring.
A045714: Primes with first digit 8.
A069675: Primes with either no internal digits or all internal digits are 0.
A081762: Primes p such that p*(p-2) divides 2^(p-1)-1.
A082108: a(n) = 4n^2 + 6n + 1.
A089392: Magnanimous primes: primes with the property that inserting a "+" in any place between two digits yields a sum which is prime.
A136065: Mother primes of order 6.
A247981: Primes dividing nonzero terms in A003095: the iterates of x^2 + 1 starting at 0.
A260147: G.f.: (1/2) * Sum_{n=-oo..+oo} x^n * (1 + x^n)^n, an even function.

Number of the day: 36507377

Properties of the number 36507377:

36507377 is a cyclic number.
36507377 = 139 × 262643 is semiprime and squarefree.
36507377 has 2 distinct prime factors, 4 divisors, 31 antidivisors and 36244596 totatives.
36507377 has a semiprime digit sum 38 in base 10.
Reversing the decimal digits of 36507377 results in a prime.
36507377 = 18253689² - 18253688² = 131391² - 131252² is the difference of 2 nonnegative squares in 2 ways.
36507377 is the sum of 2 positive triangular numbers.
36507377 is the difference of 2 positive pentagonal numbers in 2 ways.
36507377 = 13² + 38² + 6042² is the sum of 3 positive squares.
36507377² is the sum of 3 positive squares.
36507377 is a proper divisor of 557¹³¹³²¹ - 1.
36507377 is an emirpimes in (at least) the following bases: 5, 11, 12, 15, 20, 21, 22, 25, 26, 30, 34, 35, 41, 44, 45, 49, 50, 54, 55, 61, 63, 64, 65, 70, 71, 73, 74, 75, 76, 80, 85, 86, 94, 95, 97, and 99.

Number of the day: 425268

Élie Joseph Cartan was born on this day 152 years ago.

Properties of the number 425268:

425268 = 2² × 3² × 11813 is the 389470^th composite number and is not squarefree.
425268 has 3 distinct prime factors, 18 divisors, 19 antidivisors and 141744 totatives.
425268 = 106318² - 106316² = 35442² - 35436² = 11822² - 11804² is the difference of 2 nonnegative squares in 3 ways.
425268 is the difference of 2 positive pentagonal numbers in 1 way.
425268 = 282² + 588² is the sum of 2 positive squares in 1 way.
425268 = 8² + 10² + 652² is the sum of 3 positive squares.
425268² = 266220² + 331632² is the sum of 2 positive squares in 1 way.
425268² is the sum of 3 positive squares.
425268 is a proper divisor of 181²⁹⁵³ - 1.
425268 is palindromic in (at least) the following bases: 84, and -95.

Number of the day: 213881

Properties of the number 213881:

213881 is a cyclic number.
213881 is the 19116^th prime.
213881 has 15 antidivisors and 213880 totatives.
213881 has a prime digit sum 23 in base 10.
213881 = 106941² - 106940² is the difference of 2 nonnegative squares in 1 way.
213881 is the difference of 2 positive pentagonal numbers in 1 way.
213881 = 284² + 365² is the sum of 2 positive squares in 1 way.
213881 = 16² + 45² + 460² is the sum of 3 positive squares.
213881² = 52569² + 207320² is the sum of 2 positive squares in 1 way.
213881² is the sum of 3 positive squares.
213881 is a proper divisor of 1811²⁰ - 1.
213881 is an emirp in (at least) the following bases: 7, 14, 15, 16, 21, 30, 33, 35, 50, 58, 60, 61, 63, 66, 67, 69, 71, 74, 78, 82, 85, 89, 91, and 97.
213881 is palindromic in (at least) base 72.

The number 213881 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A129908: Quotient of the decimal representation of concatenated twin primes divided by 3.
A129909: Primes that are the quotient of the decimal representation of concatenated twin primes divided by 3.
A244638: In the '3x+1' problem, primes which as starting values set new records for number of steps to reach 1, where a step means either 'divide by two' or 'triple plus one and then divide by two'.

Number of the day: 1244

Properties of the number 1244:

1244 = 2² × 311 is the 1040^th composite number and is not squarefree.
1244 has 2 distinct prime factors, 6 divisors, 5 antidivisors and 620 totatives.
1244 has a prime digit sum 11 in base 10.
Reversing the decimal digits of 1244 results in a prime.
1244 = 312² - 310² is the difference of 2 nonnegative squares in 1 way.
1244 is the difference of 2 positive pentagonal numbers in 1 way.
1244 is not the sum of 3 positive squares.
1244² is the sum of 3 positive squares.
1244 is a proper divisor of 1867² - 1.
1244 is palindromic in (at least) the following bases: 12, 23, -20, and -27.
1244 in base 12 = 878 and consists of only the digits '7' and '8'.
1244 in base 22 = 2cc and consists of only the digits '2' and 'c'.
1244 in base 23 = 282 and consists of only the digits '2' and '8'.

The number 1244 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000025: Coefficients of the 3rd order mock theta function f(q).
A001749: Primes multiplied by 4.
A003368: Numbers that are the sum of 12 positive 6th powers.
A051226: Numbers m such that the Bernoulli number B_m has denominator 30.
A076042: a(0) = 0; thereafter a(n) = a(n-1) + n^2 if a(n-1) < n^2, otherwise a(n) = a(n-1) - n^2.
A085438: a(n) = Sum_{i=1..n} binomial(i+1,2)^3.
A098743: Number of partitions of n into aliquant parts (i.e., parts that do not divide n).
A126796: Number of complete partitions of n.
A292454: Numbers where 4 outnumbers any other digit.
A331683: One and all numbers of the form 2^k * prime(j) for k > 0 and j already in the sequence.

Number of the day: 4507

Properties of the number 4507:

4507 is a cyclic number.
4507 is the 611^th prime.
4507 has 7 antidivisors and 4506 totatives.
Reversing the decimal digits of 4507 results in a semiprime.
4507 = 2254² - 2253² is the difference of 2 nonnegative squares in 1 way.
4507 is the sum of 2 positive triangular numbers.
4507 is the difference of 2 positive pentagonal numbers in 1 way.
4507 = 3² + 23² + 63² is the sum of 3 positive squares.
4507² is the sum of 3 positive squares.
4507 is a proper divisor of 7⁷⁵¹ - 1.
4507 is an emirp in (at least) the following bases: 2, 3, 4, 5, 11, 14, 19, 21, 22, 37, 45, 49, 50, 51, 55, 56, 57, 61, 64, 67, 69, 71, 73, 79, 83, 84, 85, 88, and 98.
4507 is palindromic in (at least) the following bases: 25, and -53.
4507 in base 24 = 7jj and consists of only the digits '7' and 'j'.
4507 in base 25 = 757 and consists of only the digits '5' and '7'.
4507 in base 33 = 44j and consists of only the digits '4' and 'j'.

The number 4507 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003375: Numbers that are the sum of 8 positive 7th powers.
A026905: Partial sums of the partition numbers A000041.
A069832: Prefixing, suffixing or inserting a 7 in the number anywhere gives a prime.
A073520: Smallest magic constant for any n X n magic square made from consecutive primes, or 0 if no such magic square exists.
A078855: Initial term in sequence of four consecutive primes separated by 3 consecutive differences each <=6 (i.e., when d=2,4 or 6) and forming d-pattern=[6, 4,2]; short d-string notation of pattern = [642].
A112804: Primes such that the sum of the predecessor and successor primes is divisible by 19.
A118359: Primes for which the weight as defined in A117078 is 7 and the gap as defined in A001223 is 6.
A180803: T(n,k)=number of distinct solutions to sum{i=1..k}(x(2i-1)*x(2i)) == 0 (mod n), with x() in 0..n-1.
A215420: Primes that remain prime when a single digit 7 is inserted between any two consecutive digits or as the leading or trailing digit.
A217498: Primes of the form 2*n^2 + 58*n + 27.

Number of the day: 74957

Properties of the number 74957:

74957 is a cyclic number.
74957 = 23 × 3259 is semiprime and squarefree.
74957 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 71676 totatives.
Reversing the decimal digits of 74957 results in an emirpimes.
74957 = 37479² - 37478² = 1641² - 1618² is the difference of 2 nonnegative squares in 2 ways.
74957 is the difference of 2 positive pentagonal numbers in 2 ways.
74957 = 40² + 51² + 266² is the sum of 3 positive squares.
74957² is the sum of 3 positive squares.
74957 is a proper divisor of 853⁶⁶ - 1.
74957 = '7' + '4957' is the concatenation of 2 prime numbers.
74957 = '749' + '57' is the concatenation of 2 semiprime numbers.
74957 is an emirpimes in (at least) the following bases: 2, 4, 6, 8, 10, 12, 13, 14, 15, 17, 19, 20, 21, 22, 25, 29, 31, 33, 34, 35, 38, 39, 43, 45, 46, 49, 52, 53, 56, 57, 58, 59, 61, 64, 65, 74, 81, 83, 88, 91, 93, 95, 97, and 99.

The number 74957 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A158771: a(n) = 78*n^2 - 1.
A222151: Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..6 array extended with zeros and convolved with 1,-2,1
A229139: Smallest m such that Fibonacci(2n-1) = m^2 + k^2.

Number of the day: 5058135

Paul Cohen was born on this day 87 years ago.

Properties of the number 5058135:

5058135 = 3² × 5 × 112403 is the 4705869^th composite number and is not squarefree.
5058135 has 3 distinct prime factors, 12 divisors, 23 antidivisors and 2697648 totatives.
5058135 = 90³ + 112³ + 143³ is the sum of 3 positive cubes in 1 way.
5058135 = 2529068² - 2529067² = 843024² - 843021² = 505816² - 505811² = 281012² - 281003² = 168612² - 168597² = 56224² - 56179² is the difference of 2 nonnegative squares in 6 ways.
5058135 is the difference of 2 positive pentagonal numbers in 2 ways.
5058135 is not the sum of 3 positive squares.
5058135² = 3034881² + 4046508² is the sum of 2 positive squares in 1 way.
5058135² is the sum of 3 positive squares.
5058135 is a proper divisor of 101⁷⁸⁴² - 1.
5058135 = '505' + '8135' is the concatenation of 2 semiprime numbers.

Number of the day: 6457

Sophie Germain was born on this day 245 years ago.

Alexander Craig Aitken was born on this day 126 years ago.

Properties of the number 6457:

6457 is a cyclic number.
6457 = 11 × 587 is semiprime and squarefree.
6457 has 2 distinct prime factors, 4 divisors, 27 antidivisors and 5860 totatives.
6457 has a semiprime digit sum 22 in base 10.
6457 = 3229² - 3228² = 299² - 288² is the difference of 2 nonnegative squares in 2 ways.
6457 is the difference of 2 positive pentagonal numbers in 2 ways.
6457 = 7² + 18² + 78² is the sum of 3 positive squares.
6457² is the sum of 3 positive squares.
6457 is a proper divisor of 67²⁹³ - 1.
6457 is an emirpimes in (at least) the following bases: 3, 4, 5, 6, 7, 8, 9, 14, 16, 23, 24, 27, 29, 35, 37, 39, 43, 44, 51, 52, 53, 57, 58, 60, 64, 70, 75, 77, 78, 81, 85, 87, 88, 94, and 97.
6457 is palindromic in (at least) the following bases: 26, 30, and -20.
6457 in base 19 = hgg and consists of only the digits 'g' and 'h'.
6457 in base 26 = 9e9 and consists of only the digits '9' and 'e'.
6457 in base 29 = 7jj and consists of only the digits '7' and 'j'.
6457 in base 30 = 757 and consists of only the digits '5' and '7'.

The number 6457 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A006457: Number of elements in Z[ i ] whose `smallest algorithm' is <= n.
A023149: Numbers k such that prime(k) == 7 (mod k).
A025235: a(n) = (1/2)*s(n+2), where s = A014431.
A068575: Numbers n such that, as strings, n is a substring of prime(n).
A243044: T(n,k)=Number of length n+3 0..k arrays with no four elements in a row with pattern abab (with a!=b) and new values 0..k introduced in 0..k order
A264099: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 363", based on the 5-celled von Neumann neighborhood.
A266778: Molien series for invariants of finite Coxeter group A_9.
A273646: Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 817", based on the 5-celled von Neumann neighborhood.
A326235: Numbers n such that N = (35n)^6 is a twin rank (A002822: 6N +- 1 are twin primes).
A338453: Starts of runs of 3 consecutive numbers with the same total binary weight of their divisors (A093653).