A062303 Number of ways writing the n-th prime as a sum of two nonprimes.

1, 0, 1, 1, 1, 2, 2, 3, 3, 5, 6, 7, 8, 9, 9, 11, 13, 14, 15, 16, 17, 18, 19, 21, 24, 25, 26, 26, 27, 27, 33, 34, 36, 37, 40, 41, 42, 44, 45, 47, 49, 50, 53, 54, 54, 55, 59, 64, 65, 66, 66, 68, 69, 72, 74, 76, 78, 79, 80, 81, 82, 85, 91, 92, 93, 93, 99, 101, 105, 106, 106, 108

Offset: 1

Author

Labos Elemer, Jul 05 2001

Keywords

• nonn

Examples

			n=10,p(10)=29 has 14 partitions of form a+b=29; 1+28=4+25=8+21=9+20=14+15 are the 5 relevant partitions, so a(10)=5.
		

Crossrefs

Cf. A061358, A062602, A062610, A000040, A014092, A025584.

Programs

Mathematica

Table[c = 0; Do[If[i + j == Prime[n] && ! PrimeQ[i] && ! PrimeQ[j], c = c + 1], {i, Prime[n] - 1}, {j, i}]; c, {n, 72}] (* Jayanta Basu, Apr 22 2013 *)
cnpQ[{a_,b_}]:=(!PrimeQ[a]&&CompositeQ[b])||(!PrimeQ[b]&&CompositeQ[a]); Join[{1},Table[Length[Select[IntegerPartitions[Prime[n],{2}],cnpQ]],{n,2,80}]] (* Harvey P. Dale, Sep 30 2018 *)

Formula

A062610(A000040(n)) = number of [nonprime+composite] partitions of p(n).

Extensions

Offset and name corrected by Sean A. Irvine, Mar 25 2023