A331622 a(n) is the number of k such that k and n-k are both composite.

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, 13, 10, 16, 10, 19, 12, 16, 14, 19, 14, 23, 16, 21, 16, 22, 16, 27, 18, 25, 18, 25, 20, 31, 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

Offset

1,10

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Mathematics StackExchange, A question regarding the amount of composite solutions for a equation

Formula

For n >= 3, a(n) = A073610(n) + n - 3 - 2*A000720(n).

Example

a(10) = 2 because there are two k such that k and 10-k are composite, namely 4 and 6.

Maple

f:= proc(x) nops(select(t -> not isprime(t) and not isprime(x-t), [$2..x-2])) end proc:
map(f, [$1..100]);

Mathematica

a[n_] := Count[Range[4, n - 4], x_ /; CompositeQ[x] && CompositeQ[n - x]]; Array[a, 90] (* Giovanni Resta, Jan 23 2020 *)

Prog

(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

Crossrefs

Cf. A000720, A073610.

Sequence in context: A063749 A231333 A357866 * A212175 A370595 A289441

Adjacent sequences: A331619 A331620 A331621 * A331623 A331624 A331625

Keyword

nonn

Author

Robert Israel, Jan 22 2020

Status

approved