A076608 Number of nonprimes k < n such that also n-k is not a prime.

0, 1, 0, 0, 2, 0, 2, 1, 2, 4, 2, 3, 4, 4, 4, 7, 4, 7, 6, 7, 6, 10, 6, 11, 8, 12, 8, 13, 10, 15, 12, 13, 12, 18, 12, 21, 14, 16, 16, 21, 16, 23, 18, 21, 18, 24, 18, 27, 20, 27, 20, 27, 22, 31, 24, 29, 24, 32, 26, 37, 28, 30, 28, 37, 28, 41, 30, 33, 32, 41, 32, 43, 34, 40, 34, 43, 34

Offset: 1

Author

Reinhard Zumkeller, Oct 21 2002

Keywords

• nonn

Comments

a(n) is odd iff n is even and n/2 is not prime.

Convolution of A005171 with itself. - R. J. Mathar, Sep 10 2021

Examples

			5=1+4=2+3=3+2=4+1, hence a(5)=2;
6=1+5=2+4=3+3=4+2=5+1, hence a(6)=0.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A073610, A005171.

Programs

Mathematica

Table[With[{nn=m},Total[Table[If[NoneTrue[{n,nn-n},PrimeQ],1,0],{n,nn-1}]]],{m,80}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 15 2020 *)