A108098 Numbers m such that there is no k <= 2*m for which m! + k! - 1 is prime.

48, 63, 68, 74, 111, 129, 135, 161, 168, 174, 197, 236, 240, 243, 273, 279, 282, 285, 309, 322, 335, 347, 360, 393, 407, 419, 431, 437, 439, 440, 455, 460, 461, 483, 491, 494, 497, 512, 517, 522, 526, 532, 544, 567, 591, 614, 625, 650, 662, 663, 681, 687

Offset: 1

Author

Ralf Stephan, Jun 01 2005

Keywords

• nonn

Comments

For numbers m <= 320 that are not in the sequence, there exists an integer k <= 2*m such that m! + k! - 1 is a certified prime. For m > 320 the values of m! + k! - 1 are only probable primes. - Ryan Propper, Sep 02 2005

Crossrefs

Cf. A075758.

Programs

Mathematica

Do[l = Range[1, 2*n]; If[Length[Select[l, PrimeQ[n! + #! - 1]&]] == 0, Print[n]], {n, 1, 729}] (* Ryan Propper, Sep 02 2005 *)
Select[Range[700],NoneTrue[Table[#!+k!-1,{k,2#}],PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 24 2019 *)

Extensions

a(13)-a(52) from Ryan Propper, Sep 02 2005

Name edited by Jon E. Schoenfield, Nov 18 2018