A344782 Number of compositions of the n-th prime into a prime number of prime parts.

0, 0, 2, 5, 11, 23, 119, 237, 776, 6665, 16518, 207953, 892680, 1824445, 8374988, 96208461, 978217302, 2059770725, 18616884428, 78013141907, 158103168924, 1386674113487, 6734724875544, 82189835767618, 2013603833805429, 9101106147506177, 19147196940580651

Offset: 1

Author

Alois P. Heinz, May 28 2021

Keywords

• nonn

Examples

			a(3) = 2: [2,3], [3,2].
a(4) = 5: [5,2], [2,5], [3,2,2], [2,3,2], [2,2,3].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A000040, A316154, A344790.

Programs

Maple

b:= proc(n, c) option remember; `if`(n=0, `if`(isprime(c),
      1, 0), add(`if`(isprime(j), b(n-j, c+1), 0), j=2..n))
    end:
a:= n-> b(ithprime(n), 0):
seq(a(n), n=1..31);

Mathematica

b[n_, c_] := b[n, c] = If[n == 0, If[PrimeQ[c], 1, 0],
     Sum[If[PrimeQ[j], b[n - j, c + 1], 0], {j, 2, n}]];
a[n_] := b[Prime[n], 0];
Table[a[n], {n, 1, 31}] (* Jean-François Alcover, Apr 04 2022, after Alois P. Heinz *)