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

%I A334292 #23 May 05 2020 11:48:08
%S A334292 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,
%T A334292 203,223,256,277,319,521,594,723,775,1063,1135,1363,1633,1835,2191,
%U A334292 2600,2760,3644,3862,4293,4548,6261,8557,9452,9963,11000,12773,13437,17121,19774,22799
%N A334292 Number of sets of primes less than the n-th prime whose sum is the n-th prime.
%H A334292 David A. Corneth, <a href="/A334292/b334292.txt">Table of n, a(n) for n = 1..10001</a>
%F A334292 Same generating function as A111133, but on the domain of prime numbers.
%F A334292 a(n) = A070215(n) - 1. - _Jinyuan Wang_, May 04 2020
%e A334292 a(5) = 0 because 11 is the 5th prime and there are 0 sets of primes < 11 whose sum = 11.
%e A334292 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.
%o A334292 (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
%Y A334292 Cf. A000586, A070215, A111133.
%K A334292 nonn
%O A334292 1,8
%A A334292 _Gil Broussard_, Apr 21 2020
%E A334292 More terms from _David A. Corneth_, Apr 22 2020