A085507 Stirling transform of the prime characteristic function.

0, 0, 1, 4, 13, 41, 136, 505, 2171, 10693, 58246, 340242, 2095435, 13492077, 90267633, 623383765, 4414350135, 31899350954, 235002008725, 1773013299342, 13855253098226, 114135759054965, 1010686200326760, 9744658443894282, 102153128291263124, 1147158516520205256

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..576

S. K. Ghosal, J. K. Mandal, Stirling Transform Based Color Image Authentication, Procedia Technology, 2013 Volume 10, 2013, Pages 95-104.

Eric Weisstein's World of Mathematics, Stirling Transform

Formula

G.f.: Sum_{k>=1} x^prime(k)/Product_{j=1..prime(k)} (1 - j*x). - Ilya Gutkovskiy, Jun 19 2018

Maple

b:= proc(n, m) option remember;
     `if`(n=0, `if`(isprime(m), 1, 0), m*b(n-1, m)+b(n-1, m+1))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..25);  # Alois P. Heinz, Aug 06 2021

Mathematica

a[n_] := Sum[ StirlingS2[n, k]*Boole[PrimeQ[k]], {k, 0, n}]; Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Oct 29 2012 *)

Crossrefs

Sequence in context: A141364 A001453 A005002 * A121654 A186202 A036366

Adjacent sequences: A085504 A085505 A085506 * A085508 A085509 A085510

Keyword

nonn

Author

Eric W. Weisstein, Jul 02 2003

Status

approved