A053711 Numbers d such that, for some k, the upper and lower primes closest to k! are k! + d and k! - d.

1, 7, 11, 31, 397, 409, 1657, 2131, 7607

Offset

1,2

Comments

This sequence lists d = nextprime(k!) - k! = prevprime(k!) - k! for k in A053709.

Links

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

Example

For k = 10, k! = 3628800, d = 11, and the closest primes to 10! are q = 10! - 11 = 3628789 and p = 10! + 11 = 3628811. The differences d are listed here.

Mathematica

Reap[Do[If[SameQ @@ #, Sow@ First[#]] &@ Abs[# - NextPrime[#, {-1, 1}]] &[i!], {i, 200}]][[-1, -1]] (* Michael De Vlieger, Jan 14 2022 *)

Crossrefs

Cf. A033932, A033933, A006990, A037151, A006562, A053709, A053710.

Sequence in context: A236143 A084443 A228029 * A043110 A043890 A132355

Adjacent sequences: A053708 A053709 A053710 * A053712 A053713 A053714

Keyword

nonn,hard,more

Author

Labos Elemer, Feb 10 2000

Extensions

a(5)-a(8) from Donovan Johnson, Oct 12 2008

a(9) from Hans Havermann, Aug 15 2014

Status

approved