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

1,1

Comments

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

Links

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A042363 A208220 A138655 * A137070 A084730 A117696

Adjacent sequences: A053705 A053706 A053707 * A053709 A053710 A053711

Keyword

nonn,changed

Author

Labos Elemer, Feb 10 2000

Extensions

Corrected by Rick L. Shepherd, Jan 11 2006

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

Status

approved