A393674 a(n) = number of partitions of n into distinct nonprime parts, no two of which are consecutive in A018252.

1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 2, 1, 2, 2, 2, 3, 5, 2, 4, 4, 4, 6, 8, 5, 9, 10, 9, 11, 14, 11, 15, 17, 17, 19, 25, 20, 30, 30, 28, 33, 41, 37, 47, 51, 52, 58, 70, 63, 80, 87, 87, 97, 111, 106, 129, 136, 143, 155, 179, 171, 204, 218, 225, 246, 280, 273, 317, 336

Offset

0,10

Comments

See the comment at A393671.

Links

Sean A. Irvine, Table of n, a(n) for n = 0..10000

Example

a(16) counts these 5 partitions: 16, 15+1. 12+4, 10+6, 9+6+1.

Mathematica

prt[n_, sL_] := Module[{m = Length[sL], f}, If[n > Last[sL], Return["Extend sL"]];
f[i_, r_, b_] := f[i, r, b] = Which[r == 0, {{}}, r < 0 || i == 0, {}, True,
Join[f[i - 1, r, False], If[! b && s[[i]] <= r, Map[Prepend[#, sL[[i]]] &,
f[i - 1, r - sL[[i]], True]], {}]]];  Reverse[f[m, n, False]]]
z = 100;
s = Join[{1}, Select[Range[z], CompositeQ]];
m = Map[{#, prt[#, s]} &, Range[z]]
u = Map[Last, m];
Map[Length, u]
(* Peter J. C. Moses, Jan 26 2026 *)

Crossrefs

Cf. A018252, A096258, A393671, A393672, A393673, A393675, A393676.

Sequence in context: A029282 A333123 A289494 * A029286 A286221 A321347

Adjacent sequences: A393671 A393672 A393673 * A393675 A393676 A393677

Keyword

nonn

Author

Clark Kimberling, Mar 02 2026

Status

approved