A119555 - OEIS

%I #15 Jan 22 2017 10:13:04

%S 19,619,35899,3301819,

%T 468544077492065936712052044718939948687543330546977719976017418129955876663406131164377030450551575840099843957105136480237871017419158043635450756712088769133544426722033165168878328322819566779381528981882285541609256481166622331374702000809600061055686236758821446539362161635577019

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

%C 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

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

%e 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.

%p 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);

%t 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 *)

%Y Cf. A005165, A071828, A001272.

%K nonn,fini

%O 1,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, May 30 2006

%E Offset changed to 1 (this is a list) from _Bruno Berselli_, Feb 16 2012

%E Formula in name corrected by _Jens Kruse Andersen_, Jul 04 2014