A331901 Number of compositions (ordered partitions) of the n-th prime into distinct prime parts.

1, 1, 3, 3, 1, 3, 25, 9, 61, 91, 99, 151, 901, 303, 1759, 3379, 5239, 4713, 8227, 12901, 12537, 23059, 65239, 159421, 232369, 489817, 351237, 726295, 564363, 1101883, 2517865, 6916027, 11825821, 4942227, 27166753, 21280053, 39547957, 52630273, 113638975

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Index entries for sequences related to compositions

Formula

a(n) = A219107(A000040(n)).

Example

a(4) = 3 because we have [7], [5, 2] and [2, 5].

Maple

s:= proc(n) option remember; `if`(n<1, 0, ithprime(n)+s(n-1)) end:
b:= proc(n, i, t) option remember; `if`(s(i)<n, 0, `if`(n=0, t!, (p
      ->`if`(p>n, 0, b(n-p, i-1, t+1)))(ithprime(i))+b(n, i-1, t)))
    end:
a:= n-> b(ithprime(n), n, 0):
seq(a(n), n=1..42);  # Alois P. Heinz, Jan 31 2020

Mathematica

s[n_] := s[n] = If[n < 1, 0, Prime[n] + s[n - 1]];
b[n_, i_, t_] := b[n, i, t] = If[s[i] < n, 0, If[n == 0, t!, Function[p, If[p > n, 0, b[n - p, i - 1, t + 1]]][Prime[i]] + b[n, i - 1, t]]];
a[n_] := b[Prime[n], n, 0];
Array[a, 42] (* Jean-François Alcover, Nov 26 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000040, A023360, A056768, A070215, A219107, A265112, A299168.

Sequence in context: A032240 A366556 A275625 * A306148 A106836 A241235

Adjacent sequences: A331898 A331899 A331900 * A331902 A331903 A331904

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 31 2020

Status

approved