A331981 Number of compositions (ordered partitions) of n into distinct odd primes.

1, 0, 0, 1, 0, 1, 0, 1, 2, 0, 2, 1, 2, 1, 2, 6, 4, 1, 4, 7, 4, 12, 4, 13, 6, 12, 28, 18, 28, 19, 6, 25, 52, 24, 54, 30, 56, 31, 98, 156, 102, 37, 104, 157, 150, 276, 150, 175, 154, 288, 200, 528, 246, 307, 226, 666, 990, 780, 1038, 679, 348, 799, 1828, 1272, 1162, 1164

Offset

0,9

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Index entries for sequences related to compositions

Example

a(16) = 4 because we have [13, 3], [11, 5], [5, 11] and [3, 13].

Maple

s:= proc(n) option remember; `if`(n<1, 0, ithprime(n+1)+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+1))+b(n, i-1, t)))
    end:
a:= n-> b(n, numtheory[pi](n), 0):
seq(a(n), n=0..72);  # Alois P. Heinz, Feb 03 2020

Mathematica

s[n_] := s[n] = If[n < 1, 0, Prime[n + 1] + s[n - 1]];
b[n_, i_, t_] := b[n, i, t] = If[s[i] < n, 0, If[n == 0, t!, If[# > n, 0, b[n - #, i - 1, t + 1]]&[Prime[i + 1]] + b[n, i - 1, t]]];
a[n_] := b[n, PrimePi[n], 0];
a /@ Range[0, 72] (* Jean-François Alcover, Nov 09 2020, after Alois P. Heinz *)

Crossrefs

Cf. A002124, A023360, A024939, A065091, A099773, A219107, A331926, A331982.

Sequence in context: A192541 A281545 A332033 * A099302 A219198 A352513

Adjacent sequences: A331978 A331979 A331980 * A331982 A331983 A331984

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 03 2020

Status

approved