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A075409
a(n) is the smallest m such that n!-m and n!+m are both primes.
5
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
2,3
COMMENTS
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
LINKS
EXAMPLE
a(4)=5 because 4!=24 and 19 and 25 are primes with smallest distance 5 from 4!.
MATHEMATICA
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 *)
PROG
(PARI) a(n) = {my (m=0); until (ok, ok = isprime(n!-m) && isprime(n!+m); if (!ok, m++); ); return (m); } \\ Michel Marcus, Apr 19 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 18 2002
EXTENSIONS
More terms from David Wasserman, Jan 17 2005
STATUS
approved