A067365 a(n) = p-n!^5, where p is the smallest prime > n!^5+1.

2, 5, 13, 13, 7, 7, 11, 71, 23, 19, 197, 17, 101, 53, 17, 47, 73, 97, 53, 433, 251, 251, 47, 263, 281, 353, 53, 61, 179, 41, 53, 401, 449, 79, 89, 1283, 367, 2011, 139, 227, 1597, 1657, 1123, 397, 131, 727, 137, 167, 89, 379, 421, 653, 223, 373, 2221, 1447

Offset: 1

Author

Frank Buss (fb(AT)frank-buss.de), Jan 19 2002

Keywords

• nonn

Comments

The first 60 terms are primes. Are all terms prime? For n!^i, with 0

The first 1592 terms are primes. - Dana Jacobsen, May 13 2015

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..1592
• Cyril Banderier, Fortunate Numbers

Crossrefs

Cf. A037153, A037153, A005235, A067362, A067363, A067364.

Programs

Mathematica

a[n_] := For[i=2, True, i++, If[PrimeQ[n!^5+i], Return[i]]]
spf[n_]:=Module[{c=(n!)^5},NextPrime[c+1]-c]; Array[spf,60] (* Harvey P. Dale, Feb 24 2015 *)

MuPAD

for n from 1 to 50 do f := n!^5:a := nextprime(f+2)-f:print(a) end_for

PARI

for(n=1, 100, f=n!^5; print1(nextprime(f+2)-f, ", ")) \\ Dana Jacobsen, May 13 2015

Perl

use ntheory ":all"; use Math::GMP qw/:constant/; for my $n (1..500) { my $f=factorial($n)**5; say "$n ", next_prime($f+1)-$f; } # Dana Jacobsen, May 13 2015

Extensions

Edited by Dean Hickerson, Mar 02 2002

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