A130533 a(n) = smallest k such that A001358(n+1) = A001358(n) + (A001358(n) mod k), or 0 if no such k exists.

0, 0, 2, 6, 13, 9, 2, 19, 2, 19, 2, 3, 4, 37, 8, 43, 47, 47, 53, 2, 6, 59, 61, 8, 71, 6, 79, 2, 5, 83, 89, 2, 3, 12, 101, 107, 4, 3, 3, 2, 11

Offset

1,3

Comments

a(n) is the "weight" of semiprimes.

The decomposition of semiprimes into weight * level + gap is A001358(n) = a(n) * A184729(n) + A065516(n) if a(n) > 0.

Links

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

Example

For n = 1 we have A001358(n) = 4, A001358(n+1) = 6; there is no k such that 6 - 4 = 2 = (4 mod k), hence a(1) = 0.
For n = 3 we have A001358(n) = 9, A001358(n+1) = 10; 2 is the smallest k such that 10 - 9 = 1 = (9 mod k), hence a(3) = 2.
For n = 19 we have A001358(n) = 55, A001358(n+1) = 57; 53 is the smallest k such that 57 - 55 = 2 = (55 mod k), hence a(19) = 53.

Crossrefs

Cf. A001358, A065516, A184729, A184728, A117078, A117563, A001223, A118534.

Sequence in context: A161324 A226603 A116534 * A231384 A082722 A329222

Adjacent sequences: A130530 A130531 A130532 * A130534 A130535 A130536

Keyword

nonn

Author

Rémi Eismann, Aug 16 2007 - Jan 20 2011

Status

approved