A334292 Number of sets of primes less than the n-th prime whose sum is the n-th prime.

0, 0, 1, 1, 0, 1, 1, 2, 4, 6, 8, 10, 13, 14, 18, 25, 34, 38, 49, 60, 66, 86, 101, 129, 177, 203, 223, 256, 277, 319, 521, 594, 723, 775, 1063, 1135, 1363, 1633, 1835, 2191, 2600, 2760, 3644, 3862, 4293, 4548, 6261, 8557, 9452, 9963, 11000, 12773, 13437, 17121, 19774, 22799

Offset

1,8

Links

David A. Corneth, Table of n, a(n) for n = 1..10001

Formula

Same generating function as A111133, but on the domain of prime numbers.

a(n) = A070215(n) - 1. - Jinyuan Wang, May 04 2020

Example

a(5) = 0 because 11 is the 5th prime and there are 0 sets of primes < 11 whose sum = 11.
a(9) = 4 because 23 is the 9th prime and there are 4 sets of primes < 23 whose sums = 23: 13+7+3, 13+5+3+2, 11+7+5, 11+7+3+2.

Prog

(PARI) lista(nn) = {my(v, w=primes(nn)); v=Vec(prod(i=1, nn, 1+'x^w[i]) + O('x^(w[nn]+1))); for(i=1, nn, print1(v[w[i]+1]-1, ", ")); } \\ Jinyuan Wang, May 04 2020

Crossrefs

Cf. A000586, A070215, A111133.

Sequence in context: A264984 A194390 A187688 * A085884 A246404 A246408

Adjacent sequences: A334289 A334290 A334291 * A334293 A334294 A334295

Keyword

nonn

Author

Gil Broussard, Apr 21 2020

Extensions

More terms from David A. Corneth, Apr 22 2020

Status

approved