

A130650


a(n) = smallest k such that A014612(n+1) = A014612(n) + (A014612(n) mod k), or 0 if no such k exists.


7



0, 0, 4, 13, 2, 13, 18, 4, 43, 8, 3, 41, 4, 4, 3, 13, 2, 37, 16, 43, 97, 4, 9, 10, 53, 4, 5, 10, 3, 6, 61, 43, 2, 11, 2, 12, 163, 8, 13, 2, 5, 173, 8, 89, 4, 3, 37, 61, 101, 101, 107, 229, 113
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OFFSET

1,3


COMMENTS

a(n) is the "weight" of 3almost primes.
The decomposition of 3almost primes into weight * level + gap is A014612(n) = a(n) * A184753(n) + A114403(n) if a(n) > 0.


LINKS

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


EXAMPLE

For n = 1 we have A014612(1) = 8, A014612(2) = 12; there is no k such that 12  8 = 4 = (8 mod k), hence a(1) = 0.
For n = 3 we have A014612(3) = 18, A014612(4) = 20; 4 is the smallest k such that 20  18 = 2 = (18 mod k), hence a(3) = 4.
For n = 21 we have A014612(21) = 98, A014612(22) = 99; 97 is the smallest k such that 99  98 = 1 = (97 mod k), hence a(21) = 97.


CROSSREFS

Cf. A014612, A114403, A184753, A184752, A117078, A117563, A001223, A118534.
Sequence in context: A156823 A212256 A265327 * A170865 A191509 A218356
Adjacent sequences: A130647 A130648 A130649 * A130651 A130652 A130653


KEYWORD

nonn


AUTHOR

Rémi Eismann, Aug 16 2007  Jan 21 2011


STATUS

approved



