1,1

n! is an interprime: i.e. the average of two successive primes.

The difference between n! and its 2 closest primes must exceed n.

No more terms < 1000. - Hugo Pfoertner (hugo(AT)pfoertner.org), Jan 24 2005

For the 2nd term 5! is in the middle between closest neighbors 113 and 127.

for n from 3 to 200 do j := n!-prevprime(n!): if not isprime(n!+j) then next fi: i := 1: while not isprime(n!+i) and (i<=j) do i := i+2 od: if i=j then print(n):fi:od:

PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k] Do[ a = n!; If[2a == PrevPrim[a] + NextPrim[a], Print[n]], {n, 3, 415}]

Cf. A033393, A033392, A006990, A037151, A006562, A053710, A075275.

Cf. A075409 smallest m such that n!-m and n!+m are both primes.

Sequence in context: A037183 A024424 A018107 this_sequence A102772 A018005 A080522

Adjacent sequences: A053706 A053707 A053708 this_sequence A053710 A053711 A053712

nonn

Labos E. (labos(AT)ana.sote.hu), Feb 10 2000

171 and 190 from Jud McCranie (j.mccranie(AT)comcast.net), Jul 04 2000

348 from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 17 2002

a(8) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Mar 23 2008. 1638!-2131 and 1638!+2131 are 4556-digit probable primes.