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URL: https://oeis.org/A130533

⇱ A130533 - OEIS

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A130533
a(n) = smallest k such that A001358(n+1) = A001358(n) + (A001358(n) mod k), or 0 if no such k exists.
7
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
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.
KEYWORD
nonn
AUTHOR
Rémi Eismann, Aug 16 2007 - Jan 20 2011
STATUS
approved