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%I #15 Sep 08 2022 08:46:25
%S 0,0,0,0,0,0,0,1,0,2,0,3,2,4,2,5,2,7,4,7,4,8,4,11,6,10,6,11,8,15,10,
%T 13,10,16,10,19,12,16,14,19,14,23,16,21,16,22,16,27,18,25,18,25,20,31,
%U 22,27,22,30,24,37,26,30,26,35,26,39,28,33,30,39,30,43,32,40,32,41,32,47,34,43,36
%N a(n) is the number of k such that k and n-k are both composite.
%H Robert Israel, <a href="/A331622/b331622.txt">Table of n, a(n) for n = 1..10000</a>
%H Mathematics StackExchange, <a href="https://math.stackexchange.com/questions/3518988/a-question-regarding-the-amount-of-composite-solutions-for-a-equation/3519032">A question regarding the amount of composite solutions for a equation</a>
%F For n >= 3, a(n) = A073610(n) + n - 3 - 2*A000720(n).
%e a(10) = 2 because there are two k such that k and 10-k are composite, namely 4 and 6.
%p f:= proc(x) nops(select(t -> not isprime(t) and not isprime(x-t), [$2..x-2])) end proc:
%p map(f, [$1..100]);
%t a[n_] := Count[Range[4, n - 4], x_ /; CompositeQ[x] && CompositeQ[n - x]]; Array[a,90] (* _Giovanni Resta_, Jan 23 2020 *)
%o (Magma) [#[k: k in [2..n-2] | not IsPrime(k) and not IsPrime(n-k)]: n in [1..81]]; // _Marius A. Burtea_, Jan 22 2020
%Y Cf. A000720, A073610.
%K nonn
%O 1,10
%A _Robert Israel_, Jan 22 2020
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