A056752 Distance from n! to the nearest prime.

1, 0, 1, 1, 7, 1, 1, 23, 13, 11, 1, 1, 23, 1, 43, 23, 31, 37, 89, 29, 31, 31, 89, 73, 41, 37, 1, 67, 31, 1, 61, 1, 1, 97, 61, 127, 1, 1, 73, 53, 1, 79, 71, 47, 53, 89, 79, 53, 59, 61, 179, 53, 59, 127, 61, 149, 107, 109, 137, 139, 71, 71, 101, 67, 127, 283, 73, 83, 103, 97

Offset

1,5

Links

Hans Havermann, Table of n, a(n) for n = 1..2000

Example

For both 1! and 2! the nearest prime neighbor is 2, with distances of 1 and 0, respectively. The nearest primes around 8! are 40289 and 40343 with distances of 31 and 23, so a(8)=23.

Maple

with(numtheory): [seq(min(nextprime(i!)-i!, i!-prevprime(i!)), i=3..100)]; # a(1) and a(2) computed individually

Mathematica

Table[Function[k, Min[k - #, NextPrime@ # - k] &@If[n == 1, 0, Prime@ PrimePi@ k]][n!], {n, 16}] (* Michael De Vlieger, Jul 15 2017 *)

Crossrefs

Cf. A006990, A037151, A033932, A033933, A053714 (signed version with a different second term).

Sequence in context: A157272 A176200 A046739 * A053714 A168290 A218695

Adjacent sequences: A056749 A056750 A056751 * A056753 A056754 A056755

Keyword

nonn

Author

Labos Elemer, Jan 19 2001

Status

approved