Monday, January 1, 2018

Number of the day: 2018

Happy New Year!

Properties of the number 2018:

2018 = 2 × 1009 is semiprime and squarefree.
2018 has 2 distinct prime factors, 4 divisors, 9 antidivisors and 1008 totatives.
2018 has a prime digit sum 11 in base 10.
Reversing the decimal digits of 2018 results in an emirpimes.
2018 = 72 + … + 182 is the sum of at least 2 consecutive positive squares in 1 way.
2018 = 132 + 432 is the sum of 2 positive squares in 1 way.
2018 = 92 + 162 + 412 is the sum of 3 positive squares.
20182 = 11182 + 16802 is the sum of 2 positive squares in 1 way.
20182 is the sum of 3 positive squares.
2018 is a proper divisor of 15494 - 1.
2018 is an emirpimes in (at least) the following bases: 5, 8, 10, 11, 12, 13, 14, 17, 19, 21, 22, 25, 27, 29, 31, 38, 42, 45, 46, 49, 55, 57, 63, 65, 67, 69, 74, 76, 78, 80, 83, 85, 87, 90, 91, 95, 96, and 97.
2018 is palindromic in (at least) the following bases: 15, 28, -31, -32, -36, and -42.
2018 in base 3 = 2202202 and consists of only the digits '0' and '2'.
2018 in base 15 = 8e8 and consists of only the digits '8' and 'e'.
2018 in base 27 = 2kk and consists of only the digits '2' and 'k'.
2018 in base 28 = 2g2 and consists of only the digits '2' and 'g'.
2018 in base 31 = 233 and consists of only the digits '2' and '3'.
2018 in base 44 = 11c and consists of only the digits '1' and 'c'.

The number 2018 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000607: Number of partitions of n into prime parts.
A033816: a(n) = 2*n^2 + 3*n + 3.
A050053: a(n) = a(n-1)+a(m), where m=2^(p+1)+2-n and 2^p<n-1<=2^(p+1), for n >= 4.
A077068: Semiprimes of form prime + 1.
A087854: Triangle read by rows: T(n,k) is the number of n-bead necklaces with exactly k different colored beads.
A112844: Small-number statistic from the enumeration of domino tilings of a 9-pillow of order n.
A159051: Numbers n such that Fibonacci(n-2) is divisible by n.
A184535: a(n) = floor(3/5 * n^2), with a(1)=1.
A204631: Expansion of 1/(1 - x - x^2 + x^5 - x^7).
A252334: T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and column sum equal to 0 3 5 6 or 8 and every 3X3 diagonal and antidiagonal sum not equal to 0 3 5 6 or 8

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