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

Author

Ilya Gutkovskiy, Mar 17 2017

Keywords

• nonn

Examples

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

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

Crossrefs

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

Programs

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]

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

Formula

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