Tuesday, July 11, 2017

Number of the day: 1437

Properties of the number 1437:

1437 is a cyclic number.
1437 = 3 × 479 is semiprime and squarefree.
1437 has 2 distinct prime factors, 4 divisors, 13 antidivisors and 956 totatives.
1437 has an emirpimes digit sum 15 in base 10.
1437 has a triangular digit sum 15 in base 10.
Reversing the decimal digits of 1437 results in an emirpimes.
1437 = 7192 - 7182 = 2412 - 2382 is the difference of 2 nonnegative squares in 2 ways.
1437 is the sum of 2 positive triangular numbers.
1437 is the difference of 2 positive pentagonal numbers in 1 way.
1437 = 52 + 162 + 342 is the sum of 3 positive squares.
14372 is the sum of 3 positive squares.
1437 is a proper divisor of 7239 - 1.
1437 is an emirpimes in (at least) the following bases: 3, 4, 10, 11, 19, 20, 23, 29, 30, 33, 34, 35, 36, 37, 43, 45, 46, 47, 48, 49, 55, 59, 60, 63, 66, 67, 68, 69, 71, 73, 79, 82, 92, 93, and 99.
1437 is palindromic in (at least) the following bases: 12, and -35.
1437 in base 5 = 21222 and consists of only the digits '1' and '2'.
1437 in base 12 = 9b9 and consists of only the digits '9' and 'b'.
1437 in base 37 = 11V and consists of only the digits '1' and 'V'.

The number 1437 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A003037: Smallest number of complexity n: smallest number requiring n 1's to build using +, * and ^.
A032523: Index of first occurrence of n as a term in A001203, the continued fraction for Pi.
A051227: Bernoulli number B_{2n} has denominator 42.
A103471: Number of polyominoes without holes consisting of 5 regular unit n-gons.
A123142: Number of benzenoids with 23 hexagons, C_(2v) symmetry and containing n carbon atoms.
A124178: Numbers n such that 1 + n + n^3 + n^5 + n^7 + n^9 + n^11 + n^13 + n^15 + n^17 + n^19 is prime.
A191723: Dispersion of A047215, (numbers >1 and congruent to 0 or 2 mod 5), by antidiagonals.
A204867: T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly two different ways, and new values 0..1 introduced in row major order
A219852: T(n,k)=Number of nXk arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nXk array
A250167: T(n,k)=Number of length n+1 0..k arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero

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