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A053711
Numbers d such that, for some k, the upper and lower primes closest to k! are k! + d and k! - d.
4
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.
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 *)
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