A067364 a(n)=p-n!^4, where p is the smallest prime > n!^4+1.

2, 3, 5, 5, 7, 29, 19, 29, 181, 19, 31, 173, 79, 43, 379, 61, 101, 127, 101, 83, 37, 29, 271, 233, 109, 233, 293, 1039, 137, 241, 173, 197, 613, 1933, 277, 71, 503, 449, 1667, 53, 67, 163, 179, 211, 53, 613, 1171, 1069, 359, 199, 839, 433, 1523, 463, 677

Offset

1,1

Comments

The first 102 terms are primes. Are all terms prime? For n!^i, with 0<i<6, it looks like the terms are prime, too (see references). But for n!^6: a(28)=1189=29*41.

The first 1865 terms are primes. - Dana Jacobsen, May 13 2015

Links

Dana Jacobsen, Table of n, a(n) for n = 1..1865

Cyril Banderier, Fortunate Numbers

Mathematica

a[n_] := For[i=2, True, i++, If[PrimeQ[n!^4+i], Return[i]]]

Prog

(MuPAD) for n from 1 to 50 do f := n!^4:a := nextprime(f+2)-f:print(a) end_for
(PARI) for(n=1, 500, f=n!^4; 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)**4; say "$n ", next_prime($f+1)-$f; } # Dana Jacobsen, May 13 2015

Crossrefs

Cf. A037153, A037153, A005235, A067362, A067363, A067365.

Sequence in context: A094749 A096539 A338141 * A090547 A087308 A121380

Adjacent sequences: A067361 A067362 A067363 * A067365 A067366 A067367

Keyword

nonn

Author

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

Extensions

Edited by Dean Hickerson, Mar 02 2002

Status

approved