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A030281 COMPOSE natural numbers with primes.

%I A030281 #19 Feb 01 2021 18:57:42
%S A030281 2,11,53,237,1013,4196,16992,67647,265743,1032827,3979023,15217248,
%T A030281 57835016,218636365,822691425,3083074193,11512489353,42851360088,
%U A030281 159043175322,588767623587,2174488780469,8013945343961,29477541831841,108233492257428,396751988675780
%N A030281 COMPOSE natural numbers with primes.
%H A030281 Alois P. Heinz, <a href="/A030281/b030281.txt">Table of n, a(n) for n = 1..1823</a>
%H A030281 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A030281 G.f.: Sum_{j>=1} j*(Sum_{k>=1} prime(k)*x^k)^j. - _Ilya Gutkovskiy_, Apr 21 2019
%F A030281 a(n) = Sum_{k=0..n} k * A340991(n,k). - _Alois P. Heinz_, Feb 01 2021
%p A030281 b:= proc(n) option remember; `if`(n=0, [1, 0], (p->
%p A030281       p+[0, p[1]])(add(ithprime(j)*b(n-j), j=1..n)))
%p A030281     end:
%p A030281 a:= n-> b(n)[2]:
%p A030281 seq(a(n), n=1..27);  # _Alois P. Heinz_, Sep 11 2019
%t A030281 b[n_] := b[n] = If[n==0, {1, 0}, #+{0, #[[1]]}&[Sum[Prime[j] b[n-j], {j, 1, n}]]];
%t A030281 a[n_] := b[n][[2]];
%t A030281 Array[a, 27] (* _Jean-François Alcover_, Nov 09 2020, after _Alois P. Heinz_ *)
%Y A030281 Cf. A000040, A030017, A030282, A340991.
%K A030281 nonn,nice
%O A030281 1,1
%A A030281 _Christian G. Bower_