A053708 Nearest prime to n! (but not equal to n!).

2, 3, 5, 23, 113, 719, 5039, 40343, 362867, 3628789, 39916801, 479001599, 6227020777, 87178291199, 1307674368043, 20922789888023, 355687428096031, 6402373705728037, 121645100408832089, 2432902008176640029, 51090942171709439969, 1124000727777607680031, 25852016738884976639911

Offset: 1

Author

Labos Elemer, Feb 10 2000

Keywords

• nonn

Comments

If n! is the average of its closest prime neighbors then the smaller prime is to be chosen (as in A051701).

Examples

			For 8! = 40320 the closest upper and lower primes are 40289 and 40343 with d = 31 and d = 23, so 40343 is closer to 8! than the lower neighbor.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..449

Crossrefs

Cf. A000142, A033932, A037151, A033933, A006990.

Programs

Mathematica

f[n_]:=Module[{nf=n!,s,l},s=NextPrime[nf,-1];l=NextPrime[nf];If[nf-s>l-nf,l,s]]
Table[f[i],{i,25}] (* Harvey P. Dale, Dec 08 2010 *)

Extensions

Corrected by Rick L. Shepherd, Jan 11 2006

a(21)-a(23) from Amiram Eldar, Mar 10 2025