A119555 Primes in the sequence f(n) = f(n-1)+((-1)^n)*n!, with f(0)=0.

19, 619, 35899, 3301819, 468544077492065936712052044718939948687543330546977719976017418129955876663406131164377030450551575840099843957105136480237871017419158043635450756712088769133544426722033165168878328322819566779381528981882285541609256481166622331374702000809600061055686236758821446539362161635577019

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, May 30 2006

Keywords

• nonn
• fini

Comments

f(n) = (-1)^n*A005165(n). The primes are those terms in A071828 which correspond to even n values in A001272: n = 4, 6, 8, 10, 160, 4998, 9158, 11164 (the last three are only probable primes). 3612703 divides f(n) for n >= 3612702, so the sequence is finite. - Jens Kruse Andersen, Jul 04 2014

Examples

			f(0)=0, f(1) = 0+((-1)^1)*1! = -1, f(2) = -1+((-1)^2)*2! = 1, f(3) = 1+((-1)^3)*3! = -5, f(4) = -5+((-1)^4)*4! = 19, which is prime, so 19 is the first term of the sequence.
		

References

• G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 160.

Crossrefs

Cf. A005165, A071828, A001272.

Programs

Maple

P:=proc(n) local i,j; j:=0; for i from 1 by 1 to n do j:=j+((-1)^i)*i!; if isprime(j) then print(j); fi; od; end: P(100);

Mathematica

nxt[{n_,a_}]:={n+1,a+(-1)^(n+1) (n+1)!}; Select[NestList[nxt,{0,0},200][[All,2]],#>0&&PrimeQ[#]&] (* Harvey P. Dale, Jan 22 2017 *)

Extensions

Offset changed to 1 (this is a list) from Bruno Berselli, Feb 16 2012

Formula in name corrected by Jens Kruse Andersen, Jul 04 2014