A052467 Binomial transform of {b(n)}, where b(n)=1 for prime n and b(n)=0 otherwise.

0, 1, 3, 6, 11, 20, 37, 70, 134, 255, 476, 869, 1564, 2821, 5201, 9948, 19793, 40562, 84271, 174952, 359576, 728805, 1457402, 2885051, 5681277, 11185110, 22103926, 43939533, 87864092, 176447165, 354929146, 713198803, 1428312446, 2846268351

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Comments

Number of compositions of n into a prime number of parts. - Vladeta Jovovic, Jan 31 2005

The number of pernicious numbers (A052294) between 2^(n-1) and 2^n. Although the graph looks almost like 2^n, the graph of a(n)/2^n has quite a bit of variation. - T. D. Noe, Mar 14 2009

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Binomial Transform.

Crossrefs

Cf. A038499.

Cf. A010051, A121497.

Programs

Mathematica

b[n_] := Boole[ PrimeQ[n]]; a[n_] := Sum[ Binomial[n, k]*b[k], {k, 0, n}]; Table[a[n], {n, 0, 34}] // Differences (* Jean-François Alcover, Oct 25 2012 *)

Formula

G.f.: Sum_{k>=1} (x/(1 - x))^prime(k). - Ilya Gutkovskiy, Dec 28 2016

a(n) = A121497(n+1) - A121497(n). - Wesley Ivan Hurt, Jan 14 2022

Extensions

More terms from David Wasserman, Feb 25 2002

Description corrected by T. D. Noe, May 17 2003