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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 COMMENTS For n > 0 let b(n) be the inverse Euler transform of a(n). It appears that, if p is the lesser of twin primes, then b(p) = 1 and b(2*p) = -1; otherwise b(n) = 0. - Georg Fischer, Aug 15 2020 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 A331466 A166124 Adjacent sequences: A299193 A299194 A299195 * A299197 A299198 A299199 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Feb 04 2018 STATUS approved

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Last modified May 21 09:41 EDT 2024. Contains 372733 sequences. (Running on oeis4.)