A283876 Number of partitions of n into distinct twin primes (A001097).

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

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: A360821 A155124 A138033 * A365663 A067754 A194824

Adjacent sequences: A283873 A283874 A283875 * A283877 A283878 A283879

Keyword

nonn,changed

Author

Ilya Gutkovskiy, Mar 17 2017

Status

approved