A075410 -id:A075410 - cp's OEIS frontend

A075409 a(n) is the smallest m such that n!-m and n!+m are both primes.

0, 1, 5, 7, 19, 19, 31, 17, 11, 17, 83, 67, 353, 227, 163, 59, 61, 113, 353, 31, 1447, 571, 389, 191, 337, 883, 101, 1823, 659, 709, 163, 1361, 439, 307, 1093, 1733, 2491, 1063, 1091, 1999, 1439, 109, 2753, 607, 2617, 269, 103, 2663, 337, 14447, 2221, 5471, 2887

Offset: 2

Zak Seidov, Sep 18 2002

nonn

For n=3,5,10,21,171,190,348, n! is an interprime, the average of two consecutive primes, see A053709. In general n! may be average of several pairs of primes, in which case the minimal distance is in the sequence. See also n^n and n!! as average of two primes in A075468 and A075410.

According to Goldbach's conjecture, a(n) always exists with a(n) = A047160(n!). - Jens Kruse Andersen, Jul 30 2014

			a(4)=5 because 4!=24 and 19 and 25 are primes with smallest distance 5 from 4!.

Vincenzo Librandi, Table of n, a(n) for n = 2..100

Cf. A033932, A033933, A047160, A053709, A075468, A075410.

smp[n_]:=Module[{m=1,nf=n!},While[!PrimeQ[nf+m]||!PrimeQ[nf-m],m=m+2];m]; Join[{0},Array[smp,60,3]] (* Harvey P. Dale, Apr 18 2014 *)

a(n) = {my (m=0); until (ok, ok = isprime(n!-m) && isprime(n!+m); if (!ok, m++);); return (m);} \\ Michel Marcus, Apr 19 2013

More terms from David Wasserman, Jan 17 2005

A075468 Minimal m such that n^n-m and n^n+m are both primes, or -1 if there is no such m.

Original entry on oeis.org

1, 4, 15, 42, 7, 186, 75, 10, 33, 1302, 487, 114, 297, 58, 2253, 1980, 1045, 1638, 1767, 2032, 8067, 10800, 257, 588, 3423, 3334, 5907, 12882, 1213, 12972, 8547, 3644, 7035, 2178, 16747, 24324, 5523, 12628, 2241, 25602, 16495, 41706, 23127, 22376, 24927

Offset: 2

Zak Seidov, Sep 18 2002

nonn

n^n is an interprime, the average of two consecutive primes, presumably only for n = 2, 6 and 9. In general n^n may be average of several pairs of primes, in which case the minimal distance is in the sequence. It is not clear (but quite probable) that for all n, n^n is the average of two primes. See also n! and n!! as average of two primes in A075409 and A075410.

n^n -/+ a(n) are both primes, with a(n) being the smallest common distance.

			a(4)=15 because 4^4=256 and 256 -/+ 15 = 271 and 241 are primes with smallest distance from 4^4; a(23)= 10800 because 23^23 = 20880467999847912034355032910567 and 23^23 -/+ 10800 are two primes with the smallest distance from 23^23.

Sean A. Irvine, Table of n, a(n) for n = 2..150

Cf. A075469, A075409, A075410.

Cf. A000312, A082467.

fm[n_]:=Module[{n2=n^n,m=1},While[!PrimeQ[n2+m]||!PrimeQ[n2-m],m++];m]; Array[fm,50,2] (* Harvey P. Dale, May 19 2012 *)

a(n) = my(m=1,nn=n^n); while (! (ispseudoprime(nn-m) && ispseudoprime(nn+m)), m++); m; \\ Michel Marcus, Feb 21 2025

a(n) = A082467(A000312(n)). - Michel Marcus, Feb 21 2025

More terms from Lior Manor, Sep 18 2002

Corrected by Harvey P. Dale, May 19 2012

cp's OEIS Frontend

A075409 a(n) is the smallest m such that n!-m and n!+m are both primes.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions