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p - n!, where p is the fourth smallest prime > n!.
2

%I #4 Jul 24 2016 20:54:35

%S 6,9,11,17,19,23,41,41,47,47,29,83,139,79,223,149,83,101,137,79,59,

%T 131,271,283,131,263,137,197,373,313,379,137,307,151,257,761,457,151,

%U 443,89,229,167,181,191,467,1109,739,103,401,353,487,827,449,617,307

%N p - n!, where p is the fourth smallest prime > n!.

%C Is every term except the first two a prime?

%H Clark Kimberling, <a href="/A275274/b275274.txt">Table of n, a(n) for n = 1..300</a>

%e For n = 4, we have n! = 24, so that p = 41, and a(4) = 17.

%t Table[NextPrime[n!, 4] - n!, {n, 1, 150}]

%Y Cf. A275272, A000040.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jul 23 2016