Monday, February 25, 2019

Number of the day: 12902

Properties of the number 12902:

12902 = 2 × 6451 is semiprime and squarefree.
12902 has 2 distinct prime factors, 4 divisors, 17 antidivisors and 6450 totatives.
12902 has a semiprime digit sum 14 in base 10.
Reversing the decimal digits of 12902 results in a prime.
12902 = 112 + 302 + 1092 is the sum of 3 positive squares.
129022 is the sum of 3 positive squares.
12902 is a proper divisor of 13115 - 1.
12902 is an emirpimes in (at least) the following bases: 3, 4, 12, 14, 16, 21, 22, 29, 34, 39, 41, 44, 46, 47, 48, 49, 55, 58, 62, 65, 70, 72, 76, 82, 85, 87, 89, 91, 93, 96, 98, and 99.
12902 is palindromic in (at least) the following bases: 75, 97, -42, -86, and -100.
12902 in base 31 = dd6 and consists of only the digits '6' and 'd'.

The number 12902 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A017822: Expansion of 1/(1-x^3-x^4-x^5-x^6-x^7-x^8-x^9).
A080310: Rewrite 0->100 in the binary expansion of n (but leaving single zero as zero) and append 10 to the right.
A094659: Number of closed walks of length n at a vertex of the cyclic graph on 7 nodes C_7.
A098498: Number of squares on infinite half chessboard at <=n knight moves from a fixed point on the edge.
A217991: Numbers n such that n^16+1 and (n+2)^16+1 are both prime.
A227135: Partitions with parts repeated at most twice and repetition only allowed if first part has an even index (first index = 1).
A270127: Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by "Rule 86", based on the 5-celled von Neumann neighborhood.
A304709: Number of integer partitions of n whose distinct parts are pairwise coprime.
A320542: a(n) is the number of ways to select 3 distinct points forming a triangle of unsigned area = n from a square of grid points with side length n, divided by 4.

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