A091330 a(n) = ((p-1)!/p) - ((p-1)*(p-1)!/p!), where p is the n-th prime.

0, 0, 4, 102, 329890, 36846276, 1230752346352, 336967037143578, 48869596859895986086, 10513391193507374500051862068, 8556543864909388988268015483870, 10053873697024357228864849950022572972972

Offset: 1

Author

Russell Easterly, Mar 01 2004

Keywords

• nonn
• easy

Comments

Related to Wilson's Theorem. Let p be a prime number and write 1/p - (p-1)/p! = x/(p-1)!. Then x = (p-1)!/p - (p-1)*(p-1)!/p! = (p-1)!/p - (p-1)/p.

Also, a(n) = floor((p-1)!/p). [Bruno Berselli, May 31 2013]

If b(1)=1, and b(m) = ((m-1)^2 / m) *(b(m-1)+(m-3)/(m-1)) for m>1, then a(n) are the terms of b(m) for m prime. [Pedro Caceres, Dec 30 2018]

Examples

			Prime(4)=7 so a(4) = 6!/7 - 6*6!/7! = 102
		

Crossrefs

Cf. A007619.

Programs

Mathematica

A091330[n_] := Block[{p = Prime[n]}, ((p - 1)!/p) - ((p - 1)*(p - 1)!/p!)] (* Robert G. Wilson v, Mar 02 2004 *)

Extensions

More terms from Robert G. Wilson v and Ray Chandler, Mar 02 2004