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Least positive k such that !n + k is prime, where !n is left factorial.
1

%I #9 Dec 24 2019 08:29:06

%S 2,1,1,1,1,3,3,3,9,3,7,9,7,13,49,27,9,37,19,33,7,93,103,9,73,27,13,27,

%T 165,49,39,93,97,27,37,39,135,7,193,249,39,103,13,33,213,129,33,13,39,

%U 115,187,19,7,387,19,489,303,63,33,235,297,495,657,465,235,193,369,129

%N Least positive k such that !n + k is prime, where !n is left factorial.

%H Amiram Eldar, <a href="/A120621/b120621.txt">Table of n, a(n) for n = 0..1000</a>

%t a[n_] := Module[{k = 1, lf = Sum[i!, {i, 0, n - 1}]}, While[!PrimeQ[lf + k], k++]; k]; Array[a, 100, 0] (* _Amiram Eldar_, Dec 24 2019 *)

%Y Cf. A003422, A033932 (with n! instead of !n).

%K easy,nonn

%O 0,1

%A _Jason Earls_, Aug 17 2006