A119556 Primes in the sequence f(n+1) = f(n)+((-1)^(n+1))*n!, with f(1)=0.

5, 101, 4421, 1226280710981, 115578717622022981, 32656499591185747972776747396512425885838364422981, 136372385605079432248118270297843987319730859689490659519593045108637838364422981

Offset

1,1

Comments

The tenth term has 1579 digits. - Harvey P. Dale, Sep 10 2018

References

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..9

Example

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

Maple

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

Mathematica

nxt[{n_, a_}]:={n+1, a+(-1)^(n+1) n!}; Select[NestList[nxt, {1, 0}, 205][[All, 2]], #>0 && PrimeQ[#]&] (* Harvey P. Dale, Sep 10 2018 *)

Crossrefs

Sequence in context: A354332 A074790 A009757 * A009765 A113073 A349045

Adjacent sequences: A119553 A119554 A119555 * A119557 A119558 A119559

Keyword

nonn,easy

Author

Paolo P. Lava and Giorgio Balzarotti, May 30 2006

Extensions

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

Definition corrected by Harvey P. Dale, Sep 10 2018

Status

approved