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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
Eric Weisstein's World of Mathematics, Twin Primes
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
Sequence in context: A114525 A127672 A294168 * A227698 A331466 A166124
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.)