A299197 Number of partitions of n into distinct parts that are greater of twin primes (A006512).

1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 2, 1, 0, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 2, 0, 0, 1, 1, 3, 1, 1, 0, 0, 2, 3, 2, 0, 0, 1, 2, 3, 2, 1, 0, 0, 2, 3, 3, 0, 0, 0, 1, 4, 3, 1, 0, 0, 2, 3, 3, 2, 0, 0, 1, 4, 4

Offset

0,32

Links

Table of n, a(n) for n=0..105.

Eric Weisstein's World of Mathematics, Twin Primes

Index entries for related partition-counting sequences

Formula

G.f.: Product_{k>=1} (1 + x^A006512(k)).

Example

a(31) = 2 because we have [31] and [19, 7, 5].

Mathematica

nmax = 105; CoefficientList[Series[Product[1 + Boole[PrimeQ[k] && PrimeQ[k - 2]] x^k, {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A000586, A000607, A001097, A006512, A077608, A129363, A283875, A283876, A299196.

Sequence in context: A298246 A279024 A213731 * A334196 A143111 A328361

Adjacent sequences: A299194 A299195 A299196 * A299198 A299199 A299200

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2018

Status

approved