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

%I A067364 #15 Apr 25 2016 11:45:29
%S A067364 2,3,5,5,7,29,19,29,181,19,31,173,79,43,379,61,101,127,101,83,37,29,
%T A067364 271,233,109,233,293,1039,137,241,173,197,613,1933,277,71,503,449,
%U A067364 1667,53,67,163,179,211,53,613,1171,1069,359,199,839,433,1523,463,677
%N A067364 a(n)=p-n!^4, where p is the smallest prime > n!^4+1.
%C A067364 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.
%C A067364 The first 1865 terms are primes. - _Dana Jacobsen_, May 13 2015
%H A067364 Dana Jacobsen, <a href="/A067364/b067364.txt">Table of n, a(n) for n = 1..1865</a>
%H A067364 Cyril Banderier, <a href="http://algo.inria.fr/banderier/Computations/prime_factorial.html">Fortunate Numbers</a>
%t A067364 a[n_] := For[i=2, True, i++, If[PrimeQ[n!^4+i], Return[i]]]
%o A067364 (MuPAD) for n from 1 to 50 do f := n!^4:a := nextprime(f+2)-f:print(a) end_for
%o A067364 (PARI) for(n=1, 500, f=n!^4; print1(nextprime(f+2)-f, ", ")) \\ _Dana Jacobsen_, May 13 2015
%o A067364 (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
%Y A067364 Cf. A037153, A037153, A005235, A067362, A067363, A067365.
%K A067364 nonn
%O A067364 1,1
%A A067364 Frank Buss (fb(AT)frank-buss.de), Jan 19 2002
%E A067364 Edited by _Dean Hickerson_, Mar 02 2002