A130703 a(n) = smallest k such that A000217(n+1) = A000217(n) + (A000217(n) mod k), or 0 if no such k exists.

0, 0, 0, 0, 9, 14, 10, 27, 35, 22, 18, 65, 77, 18, 26, 119, 27, 38, 34, 27, 209, 46, 28, 55, 299, 36, 35, 377, 45, 62, 58, 45, 527, 40, 54, 629, 95, 54, 74, 779, 63, 86, 82, 63, 989, 94, 54, 161, 235, 68, 91, 265, 81, 65, 106, 81, 145, 118, 90, 1769, 1829

Offset: 1

Author

Rémi Eismann, Aug 16 2007 - Jan 10 2011

Keywords

• nonn

Comments

a(n) is the weight of triangular numbers.

The decomposition of triangular numbers into weight * level + gap is A000217(n) = a(n) * A184219(n) + (n + 1) if a(n) > 0.

Examples

			For n = 1 we have A000217(n) = 1, A000217(n+1) = 3; there is no k such that 3 - 1 = 2 = (1 mod k), hence a(1) = 0.
For n = 5 we have A000217(n) = 15, A000217(n+1) = 21; 9 is the smallest k such that 21 - 15 = 6 = (15 mod k), hence a(5) = 9.
For n = 22 we have A000217(n) = 253, A000217(n+1) = 276; 46 is the smallest k such that 276 - 253 = 23 = (253 mod k), hence a(22) = 46.
		

Links

• Remi Eismann, Table of n, a(n) for n=1..9999

Crossrefs

Cf. A020639, A117078, A117563, A001223, A118534, A090369, A090368.