A067363 a(n)=p-n!^3, where p is the smallest prime > n!^3+1.

2, 3, 7, 5, 17, 11, 17, 23, 23, 103, 59, 17, 29, 79, 59, 23, 347, 307, 53, 227, 131, 83, 67, 223, 29, 59, 197, 83, 181, 293, 71, 71, 139, 43, 67, 103, 431, 743, 1279, 197, 419, 127, 271, 73, 229, 503, 211, 181, 1597, 151, 151, 197, 1013, 179, 587, 71, 137, 547

Offset: 1

Author

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

Keywords

• nonn

Comments

The first 118 terms are primes. Are all terms prime? For n!^i, with 0

The first 2278 terms are primes. - Dana Jacobsen, May 13 2015

Links

• Dana Jacobsen, Table of n, a(n) for n = 1..2278
• Cyril Banderier, Fortunate Numbers

Crossrefs

Cf. A037153, A037153, A005235, A067362, A067364, A067365.

Programs

Mathematica

a[n_] := For[i=2, True, i++, If[PrimeQ[n!^3+i], Return[i]]]
spn[n_]:=Module[{c=(n!)^3},NextPrime[c+1]-c]; Array[spn,60] (* Harvey P. Dale, May 25 2023 *)

MuPAD

for n from 1 to 50 do f := n!^3:a := nextprime(f+2)-f:print(a) end_for

PARI

for(n=1, 100, f=n!^3; 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)**3; say "$n ", next_prime($f+1)-$f; } # Dana Jacobsen, May 13 2015

Extensions

Edited by Dean Hickerson, Mar 02 2002

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