A073308 Numbers k such that k! + k + 1 is prime.

0, 1, 2, 4, 6, 10, 52, 6822, 30838

Offset

1,3

Comments

Clearly, for k>2, k != 2 (mod 3).

Often m! + 2, m! + 3, ..., m! + m is cited as a constructed sequence of m-1 consecutive composite numbers.

Except for 0, k+1 is prime. - Robert Israel, Jan 13 2015

References

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 52, p. 20, Ellipses, Paris 2008.

Links

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

Formula

a(n) = A092791(n) - 1. - Seiichi Manyama, Mar 19 2018

Mathematica

f[n_]:=n!+n+1; lst={}; Do[p=f[n]; If[PrimeQ[p], AppendTo[lst, n]], {n, 0, 2*5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 02 2009 *)

Prog

(PARI) for(n=0, 1960, if(isprime(n!+n+1), print1(n, ", ")))

Crossrefs

Cf. A073309 (corresponding primes), A002981 (n!+1 is prime), A073443 (n!-n-1 is prime), A092791.

Sequence in context: A171447 A207667 A085809 * A058960 A036053 A237816

Adjacent sequences: A073305 A073306 A073307 * A073309 A073310 A073311

Keyword

nonn,more

Author

Rick L. Shepherd, Jul 24 2002

Extensions

a(8) from T. D. Noe, Jan 18 2008

a(9) from Seiichi Manyama (by using the data calculated by Giovanni Resta, May 04 2013), Mar 19 2018

Status

approved