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a(n) = smallest number > a(n-1) such that a(1)*a(2)*...*a(n) - 1 is a prime.
5

%I #20 Oct 14 2021 18:13:02

%S 3,4,5,6,8,9,11,14,18,20,21,27,28,37,62,77,86,97,100,107,109,166,167,

%T 181,196,225,262,266,268,274,278,290,305,345,378,385,414,429,438,442,

%U 498,503,516,531,573,595,596,611,640,665,749,794,870

%N a(n) = smallest number > a(n-1) such that a(1)*a(2)*...*a(n) - 1 is a prime.

%H Amiram Eldar, <a href="/A051957/b051957.txt">Table of n, a(n) for n = 1..1000</a> (terms 1..200 from T. D. Noe)

%t seq={3};Do[n=Last[seq]+1;While[!PrimeQ[n Times@@seq-1],n++]; AppendTo[ seq,n];,{60}];seq (* _Harvey P. Dale_, Oct 21 2011 *)

%Y Cf. A046966, A051956.

%K nice,nonn

%O 1,1

%A _Felice Russo_, Dec 21 1999