A087147 Numbers k such that k!+(k+1)!+1 is prime.

0, 3, 7, 9, 67, 291, 1343, 6984, 12861

Offset

1,2

Comments

291 is in the sequence and also is in the sequence A087146, thus (291!+292!-1,291!+292!+1) is a twin pair of primes. Any additional terms are greater than 1800 with the next prime having more than 5086 digits.

Next term is greater than 4200. - Gabriel Cunningham (gcasey(AT)mit.edu), Sep 09 2003

a(10) > 25000. - Robert Price, Aug 26 2015

k+1 is not prime because (p-1)! + p! + 1 == 0 mod p and (p-1)! + p! + 1 > p where p is prime. - Seiichi Manyama, Mar 22 2018

References

H. Dubner, Factorial and primorial primes, J. Rec. Math., 19 (No.3, 1987)

Links

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

Eric Weisstein's World of Mathematics, Wilson's Theorem

Example

3 is in the sequence because 3!+4!+1=31 is prime.

Mathematica

v={}; Do[If[PrimeQ[n!+(n+1)!+1], v=Append[v, n]; Print[v]], {n, 1800}]; v
Select[Range[0, 25000], PrimeQ[#!+(#+1)!+1]&] (* Robert Price, Aug 26 2015 *)

Prog

(PARI) isok(k) = ispseudoprime(k!+(k+1)!+1); \\ Altug Alkan, Mar 22 2018

Crossrefs

Cf. A087146, A051856.

Primes in A118913. [From Dmitry Kamenetsky, Oct 21 2008]

Sequence in context: A088801 A003033 A193945 * A363572 A337613 A152607

Adjacent sequences: A087144 A087145 A087146 * A087148 A087149 A087150

Keyword

more,nonn

Author

Farideh Firoozbakht, Aug 19 2003

Extensions

a(8)-a(9) from Robert Price, Aug 26 2015

Status

approved