A030281 COMPOSE natural numbers with primes.

2, 11, 53, 237, 1013, 4196, 16992, 67647, 265743, 1032827, 3979023, 15217248, 57835016, 218636365, 822691425, 3083074193, 11512489353, 42851360088, 159043175322, 588767623587, 2174488780469, 8013945343961, 29477541831841, 108233492257428, 396751988675780

Offset: 1

Author

Christian G. Bower

Keywords

• nonn
• nice

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1823
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000040, A030017, A030282, A340991.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, [1, 0], (p->
      p+[0, p[1]])(add(ithprime(j)*b(n-j), j=1..n)))
    end:
a:= n-> b(n)[2]:
seq(a(n), n=1..27);  # Alois P. Heinz, Sep 11 2019

Mathematica

b[n_] := b[n] = If[n==0, {1, 0}, #+{0, #[[1]]}&[Sum[Prime[j] b[n-j], {j, 1, n}]]];
a[n_] := b[n][[2]];
Array[a, 27] (* Jean-François Alcover, Nov 09 2020, after Alois P. Heinz *)

Formula

G.f.: Sum_{j>=1} j*(Sum_{k>=1} prime(k)*x^k)^j. - Ilya Gutkovskiy, Apr 21 2019

a(n) = Sum_{k=0..n} k * A340991(n,k). - Alois P. Heinz, Feb 01 2021