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

1,3

Links

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

Example

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

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 *)

Crossrefs

Cf. A000040, A316154, A344790.

Sequence in context: A201779 A067149 A354150 * A191240 A208952 A091358

Adjacent sequences: A344779 A344780 A344781 * A344783 A344784 A344785

Keyword

nonn

Author

Alois P. Heinz, May 28 2021

Status

approved