A184753 -id:A184753 - cp's OEIS frontend

A130650 a(n) = smallest k such that A014612(n+1) = A014612(n) + (A014612(n) mod k), or 0 if no such k exists.

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

Offset: 1

Rémi Eismann, Aug 16 2007 - Jan 21 2011

nonn

a(n) is the "weight" of 3-almost primes.

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

			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.

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

Cf. A014612, A114403, A184753, A184752, A117078, A117563, A001223, A118534.

A184752 a(n) = largest k such that A014612(n+1) = A014612(n) + (A014612(n) mod k), or 0 if no such k exists.

Original entry on oeis.org

0, 0, 16, 13, 26, 26, 18, 40, 43, 40, 48, 41, 60, 64, 66, 65, 74, 74, 64, 86, 97, 96, 99, 100, 106, 112, 115, 110, 123, 120, 122, 129, 146, 143, 152, 144, 163, 160, 169, 170, 170, 173, 168, 178, 184, 186, 185, 183, 202, 202, 214

Offset: 1

Rémi Eismann, Jan 21 2011

nonn

From the definition, a(n) = A014612(n) - A114403(n) if A014612(n) - A114403(n) > A114403(n), 0 otherwise where A014612 are the 3-almost primes and A114403 are the gaps between 3-almost primes.

			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; 16 is the largest k such that 20 - 18 = 2 = (18 mod k), hence a(3) = 16.
For n = 21 we have A014612(21) = 98, A014612(22) = 99; 97 is the largest k such that 99 - 98 = 1 = (97 mod k), hence a(21) = 97.

Rémi Eismann, Table of n, a(n) for n = 1..10000

Cf. A014612, A114403, A130650, A184753, A117078, A117563, A001223, A118534.

cp's OEIS Frontend

A130650 a(n) = smallest k such that A014612(n+1) = A014612(n) + (A014612(n) mod k), or 0 if no such k exists.

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