cp's OEIS Frontend

A341982 Number of ways to write n as an ordered sum of 2 primes (counting 1 as a prime).

%I A341982 #14 Sep 16 2022 21:44:59
%S A341982 1,2,3,2,3,2,4,2,3,0,4,2,5,2,4,0,6,2,6,2,5,0,8,2,5,0,4,0,8,2,6,2,7,0,
%T A341982 8,0,5,2,6,0,10,2,8,2,7,0,12,2,8,0,6,0,12,2,6,0,7,0,14,2,7,2,10,0,12,
%U A341982 0,6,2,10,0,14,2,11,2,10,0,14,0,10,2,9,0,18,2,9,0,8
%N A341982 Number of ways to write n as an ordered sum of 2 primes (counting 1 as a prime).
%H A341982 Alois P. Heinz, <a href="/A341982/b341982.txt">Table of n, a(n) for n = 2..10000</a>
%F A341982 G.f.: ( x + Sum_{k>=1} x^prime(k) )^2.
%p A341982 b:= proc(n) option remember; series(`if`(n=0, 1, x*add(
%p A341982       `if`(j=1 or isprime(j), b(n-j), 0), j=1..n)), x, 3)
%p A341982     end:
%p A341982 a:= n-> coeff(b(n), x, 2):
%p A341982 seq(a(n), n=2..88);  # _Alois P. Heinz_, Feb 24 2021
%t A341982 nmax = 88; CoefficientList[Series[(x + Sum[x^Prime[k], {k, 1, nmax}])^2, {x, 0, nmax}], x] // Drop[#, 2] &
%Y A341982 Cf. A008578, A073610, A096139, A280917, A283762, A341945, A341973, A341983, A341984.
%K A341982 nonn
%O A341982 2,2
%A A341982 _Ilya Gutkovskiy_, Feb 24 2021