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A283876 Number of partitions of n into distinct twin primes (A001097). 5
1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 4, 2, 4, 4, 3, 4, 4, 5, 4, 4, 5, 5, 5, 5, 6, 6, 5, 7, 6, 8, 7, 7, 9, 7, 9, 8, 9, 9, 9, 9, 11, 11, 11, 12, 11, 14, 12, 13, 14, 14, 13, 15, 15, 17, 16, 16, 19, 17, 20, 19, 21, 21, 21, 21, 23, 23, 23, 23, 24, 26, 25, 28, 28, 30, 29, 30, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,17

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Twin Primes

Index entries for related partition-counting sequences

FORMULA

G.f.: Product_{k>=1} (1 + x^A001097(k)).

EXAMPLE

a(29) = 4 because we have [29], [19, 7, 3], [17, 7, 5] and [13, 11, 5].

MATHEMATICA

nmax = 95; CoefficientList[Series[Product[1 + Boole[PrimeQ[k] && (PrimeQ[k - 2] || PrimeQ[k + 2])] x^k, {k, 1, nmax}], {x, 0, nmax}], x]

PROG

(PARI) listA001097(lim)=my(v=List([3]), p=5); forprime(q=7, lim, if(q-p==2, listput(v, p); listput(v, q)); p=q); if(p+2>lim && isprime(p+2), listput(v, p)); Vec(v)

first(n)=my(v=listA001097(n), x=O('x^(n+1))+'x); Vec(prod(i=1, #v, 1+x^v[i]))[1..n+1] \\ Charles R Greathouse IV, Mar 17 2017

(PARI) Vec(prod(k=1, 95, (1 + (isprime(k) && (isprime(k - 2) || isprime(k + 2)))*x^k)) + O(x^96)) \\ Indranil Ghosh, Mar 17 2017

CROSSREFS

Cf. A000586, A001097, A077608, A129363, A283875.

Sequence in context: A156642 A155124 A138033 * A067754 A194824 A339931

Adjacent sequences: A283873 A283874 A283875 * A283877 A283878 A283879

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 17 2017

STATUS

approved

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Last modified November 26 14:12 EST 2022. Contains 358362 sequences. (Running on oeis4.)