cp's OEIS Frontend

A334207 Number of ways to write 2n as the sum of two nonprime positive integers.

%I A334207 #15 Jun 15 2020 23:42:46
%S A334207 1,0,0,1,2,2,2,4,4,4,5,6,6,7,8,7,9,11,8,11,12,11,12,14,14,14,16,15,16,
%T A334207 19,15,19,21,17,21,22,20,22,25,22,23,27,24,25,30,26,27,31,27,31,33,30,
%U A334207 31,34,32,34,37,34,34,42,34,37,43,36,41,43,40,41,44,43
%N A334207 Number of ways to write 2n as the sum of two nonprime positive integers.
%H A334207 Robert Israel, <a href="/A334207/b334207.txt">Table of n, a(n) for n = 1..10000</a>
%H A334207 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A334207 a(n) = Sum_{i=1..n} (1 - c(i)) * (1 - c(2*n - i)), where c is the prime characteristic (A010051).
%e A334207 a(8) = 4; 2*8 = 16 has four partitions into nonprime parts, (15,1), (12,4), (10,6) and (8,8).
%p A334207 N:= 1000: # for a(1)..a(N)
%p A334207 NP:= remove(isprime, [$1..2*N]):
%p A334207 V:= Vector(N):
%p A334207 for i from 1 to nops(NP) do
%p A334207   for j from i do
%p A334207     x:= NP[i]+NP[j];
%p A334207     if x > 2*N then break fi;
%p A334207     if x::even then
%p A334207       V[x/2]:= V[x/2]+1;
%p A334207     fi
%p A334207 od od:
%p A334207 convert(V,list); # _Robert Israel_, Apr 20 2020
%t A334207 Table[Sum[(1 - PrimePi[i] + PrimePi[i - 1]) (1 - PrimePi[2 n - i] + PrimePi[2 n - i - 1]), {i, n}], {n, 100}]
%Y A334207 Cf. A010051.
%Y A334207 Bisection of A062610.
%K A334207 nonn,easy
%O A334207 1,5
%A A334207 _Wesley Ivan Hurt_, Apr 18 2020