A067362 a(n) = p - n!^2, where p is the smallest prime > n!^2+1.

2, 3, 5, 11, 7, 11, 11, 13, 23, 17, 13, 59, 23, 31, 23, 41, 59, 67, 29, 31, 103, 389, 59, 107, 47, 127, 67, 181, 101, 97, 409, 37, 61, 43, 61, 47, 263, 109, 53, 199, 167, 337, 47, 131, 127, 73, 181, 257, 191, 101, 83, 79, 181, 167, 229, 859, 421, 433, 107, 971

Offset

1,1

Comments

The first 157 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 200 terms are primes. - Jon Perry and Christ van Willegen, Mar 07 2003

The first 3003 terms are primes. - Dana Jacobsen, May 13 2015

Links

Dana Jacobsen, Table of n, a(n) for n = 1..3000

Cyril Banderier, Fortunate Numbers

Mathematica

a[n_] := For[i=2, True, i++, If[PrimeQ[n!^2+i], Return[i]]]
Table[p = NextPrime[(x = (n!)^2) + 1]; p - x, {n, 60}] (* Jayanta Basu, Aug 10 2013 *)

Prog

(MuPAD) for n from 1 to 50 do f := n!^2:a := nextprime(f+2)-f:print(a) end_for
(PARI) for(n=1, 500, f=n!^2; print1(nextprime(f+2)-f, ", ")) \\  Dana Jacobsen, May 10 2015
(Perl) use ntheory ":all"; use Math::GMP qw/:constant/; for my $n (1..500) { my $f=factorial($n)**2; say "$n ", next_prime($f+1)-$f; } # Dana Jacobsen, May 10 2015

Crossrefs

Cf. A037153, A037153, A005235, A067363, A067364, A067365.

Sequence in context: A259387 A130165 A083397 * A364201 A248793 A131200

Adjacent sequences: A067359 A067360 A067361 * A067363 A067364 A067365

Keyword

nonn

Author

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

Extensions

Edited by Dean Hickerson, Mar 02 2002

Status

approved