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A233746 a(1) = 3; for n>3, a(n) = smallest number > a(n-1) such that a(1)*a(2)*...*a(n) + 1 is nonprime.

%I A233746 #9 Jun 19 2019 02:45:06
%S A233746 3,5,6,8,10,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,
%T A233746 31,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,
%U A233746 55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73
%N A233746 a(1) = 3; for n>3, a(n) = smallest number > a(n-1) such that a(1)*a(2)*...*a(n) + 1 is nonprime.
%C A233746 The numbers 1, 2, 4, 7, 9, 11, 32, 322, 498, 685, 880, ... are not in the sequence.
%H A233746 Robert Israel, <a href="/A233746/b233746.txt">Table of n, a(n) for n = 1..2000</a>
%e A233746 3+1 = 4, 3*5+1 = 16, 3*5*6+1 = 91, 3*5*6*8+1 = 721, etc. are nonprimes.
%p A233746 A[1]:= 3: P:= 3:
%p A233746 for n from 2 to 100 do
%p A233746   for k from A[n-1]+1 do
%p A233746     if not isprime(P*k+1) then
%p A233746       A[n]:= k; P:= P*k; break
%p A233746     fi
%p A233746 od od:
%p A233746 seq(A[i],i=1..100); # _Robert Israel_, Jun 18 2019
%t A233746 seq={3};Do[n=Last[seq]+1;While[PrimeQ[n Times@@seq+1],n++];AppendTo[seq,n];,{100}];seq
%Y A233746 Cf. A083769, A233745.
%K A233746 nonn
%O A233746 1,1
%A A233746 _Michel Lagneau_, Dec 15 2013