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%I #9 Nov 21 2013 12:48:00
%S 3,3,5,5,11,7,11,11,29,29,13,71,29,19,19,37,23,23,41,29,53,53,89,29,
%T 41,41,59,227,79,41,101,73,61,41,37,59,67,127,67,223,71,43,53,71,71,
%U 113,239,71,313,157
%N Let q_n be least prime > x_n := 1 + 2*n!; sequence gives a(n) = q_n-x_n+1.
%F a(n)=nextprime(2*n!+1)-2*n!, where nextprime is A151800.
%e a(4) = 5 because 2*4!+1=49, the next prime is 51 and the difference between 53 and 48 is 13.
%t Do[If[PrimeQ[NextPrime[2*n!+1]-2*n! ], Print[n]], {n, 100}]
%t f[x_]:=Module[{n=2x!},NextPrime[n+1]-n]
%t f/@Range[60] (* _Harvey P. Dale_, Feb 14 2011 *)
%o (PARI) vector(100,n,nextprime(2*n!+2)-2*n!) \\ _Charles R Greathouse IV_, Feb 14 2011
%K hard,nonn
%O 1,1
%A Maciej Ulas (maciejulas(AT)poczta.onet.pl), Apr 25 2003