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

%I A067362 #25 Apr 25 2016 11:45:29
%S A067362 2,3,5,11,7,11,11,13,23,17,13,59,23,31,23,41,59,67,29,31,103,389,59,
%T A067362 107,47,127,67,181,101,97,409,37,61,43,61,47,263,109,53,199,167,337,
%U A067362 47,131,127,73,181,257,191,101,83,79,181,167,229,859,421,433,107,971
%N A067362 a(n) = p - n!^2, where p is the smallest prime > n!^2+1.
%C A067362 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.
%C A067362 The first 200 terms are primes. - _Jon Perry_ and Christ van Willegen, Mar 07 2003
%C A067362 The first 3003 terms are primes. - _Dana Jacobsen_, May 13 2015
%H A067362 Dana Jacobsen, <a href="/A067362/b067362.txt">Table of n, a(n) for n = 1..3000</a>
%H A067362 Cyril Banderier, <a href="http://algo.inria.fr/banderier/Computations/prime_factorial.html">Fortunate Numbers</a>
%t A067362 a[n_] := For[i=2, True, i++, If[PrimeQ[n!^2+i], Return[i]]]
%t A067362 Table[p = NextPrime[(x = (n!)^2) + 1]; p - x, {n, 60}] (* _Jayanta Basu_, Aug 10 2013 *)
%o A067362 (MuPAD) for n from 1 to 50 do f := n!^2:a := nextprime(f+2)-f:print(a) end_for
%o A067362 (PARI) for(n=1,500,f=n!^2;print1(nextprime(f+2)-f, ", ")) \\  _Dana Jacobsen_, May 10 2015
%o A067362 (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
%Y A067362 Cf. A037153, A037153, A005235, A067363, A067364, A067365.
%K A067362 nonn
%O A067362 1,1
%A A067362 Frank Buss (fb(AT)frank-buss.de), Jan 19 2002
%E A067362 Edited by _Dean Hickerson_, Mar 02 2002