A344789 Number of partitions of the n-th nonprime number into a nonprime number of nonprime parts.

1, 2, 2, 2, 4, 3, 6, 8, 11, 11, 19, 27, 32, 37, 55, 63, 78, 88, 108, 149, 204, 232, 274, 313, 371, 497, 556, 654, 864, 1135, 1267, 1476, 1915, 2142, 2474, 2754, 3182, 4070, 4528, 5190, 5769, 6594, 8347, 10530, 11666, 13240, 14657, 16597, 20747, 22924, 25854

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..5000

Example

a(5) = 4: [9], [6,1,1,1], [4,1,1,1,1,1], [1,1,1,1,1,1,1,1,1].
a(6) = 3: [10], [4,4,1,1], [1,1,1,1,1,1,1,1,1,1].
a(7) = 6: [12], [9,1,1,1], [6,4,1,1], [4,4,1,1,1,1], [4,1,1,1,1,1,1,1,1], [1,1,1,1,1,1,1,1,1,1,1,1].

Maple

c:= proc(n) option remember; local k; if n=1 then 1 else
      for k from 1+c(n-1) while isprime(k) do od; k fi
    end:
h:= proc(n) option remember; `if`(isprime(n), h(n-1), n) end:
b:= proc(n, i, c) option remember; `if`(n=0 or i=1, `if`(isprime(
      c+n), 0, 1), b(n-i, h(min(n-i, i)), c+1)+b(n, h(i-1), c))
    end:
a:= n-> b(c(n)$2, 0):
seq(a(n), n=1..55);

Mathematica

c[n_] := c[n] = Module[{k}, If[n == 1, 1,
   For[k = 1+c[n-1], PrimeQ[k], k++]; k]];
h[n_] := h[n] = If[PrimeQ[n], h[n-1], n];
b[n_, i_, c_] := b[n, i, c] = If[n == 0 || i == 1, If[PrimeQ[
   c+n], 0, 1], b[n-i, h[Min[n-i, i]], c+1] + b[n, h[i-1], c]];
a[n_] := b[c[n], c[n], 0];
Table[a[n], {n, 1, 55}] (* Jean-François Alcover, Sep 08 2022, after Alois P. Heinz *)

Crossrefs

Cf. A018252, A316154.

Sequence in context: A368689 A210596 A240078 * A228660 A228796 A155837

Adjacent sequences: A344786 A344787 A344788 * A344790 A344791 A344792

Keyword

nonn

Author

Alois P. Heinz, May 28 2021

Status

approved