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A299196 Number of partitions of n into distinct parts that are lesser of twin primes (A001359). 2
1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 2, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 0, 2, 1, 0, 2, 1, 1, 3, 2, 1, 3, 2, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 2, 3, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,47

LINKS

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

Ilya Gutkovskiy, Scatter plot of a(n) - A299197(n)

Eric Weisstein's World of Mathematics, Twin Primes

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=1} (1 + x^A001359(k)).

EXAMPLE

a(46) = 2 because we have [41, 5] and [29, 17].

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, A001359, A077608, A129363, A283875, A283876, A299197.

Sequence in context: A114525 A127672 A294168 * A227698 A166124 A134979

Adjacent sequences:  A299193 A299194 A299195 * A299197 A299198 A299199

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 04 2018

STATUS

approved

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Last modified June 21 15:14 EDT 2018. Contains 305622 sequences. (Running on oeis4.)