A133151 a(n) = smallest k such that A000326(n+1) = A000326(n) + (A000326(n) mod k), or 0 if no such k exists.

0, 0, 0, 0, 19, 32, 24, 67, 89, 38, 71, 173, 69, 61, 71, 109, 373, 211, 79, 529, 587, 72, 89, 779, 283, 461, 499, 359, 1159, 311, 111, 1423, 1517, 269, 857, 1817, 641, 127, 134, 251, 2377, 1249, 138, 2749, 2879, 251, 787, 173, 381, 1787, 1861, 1291

Offset: 1

Author

Rémi Eismann, Sep 22 2007 - Jan 21 2011

Keywords

• nonn

Comments

a(n) is the "weight" of pentagonal numbers (A000326).

The decomposition of pentagonal numbers into weight * level + gap is A000326(n) = a(n) * A184751(n) + A016777(n) if a(n) > 0.

Examples

			For n = 1 we have A000326(n) = 1, A000326(n+1) = 5; there is no k such that 5 - 1 = 4 = (1 mod k), hence a(1) = 0.
For n = 5 we have A000326(n) = 35, A000326(n+1) = 51; 19 is the smallest k such that 51 - 35 = 16 = (35 mod k), hence a(5) = 19.
For n = 18 we have A000326(n) = 477, A000326(n+1) = 532; 211 is the smallest k such that 532 - 477 = 55 = (477 mod k), hence a(18) = 211.
		

Links

• Remi Eismann, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000326, A016777, A184751, A184750, A117078, A117563, A001223, A118534.