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

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1823

N. J. A. Sloane, Transforms

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

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 *)

Crossrefs

Cf. A000040, A030017, A030282, A340991.

Sequence in context: A333542 A168022 A355974 * A289847 A063767 A307568

Adjacent sequences: A030278 A030279 A030280 * A030282 A030283 A030284

Keyword

nonn,nice

Author

Christian G. Bower

Status

approved