%I #10 Jun 16 2019 22:30:42
%S 5,7,17,23,37,53,157,163,173,193,227,233,257,263,283,353,383,397,457,
%T 487,523,557,563,607,677,683,733,787,823,857,863,877,947,983,997,1033,
%U 1097,1117,1153,1187,1193,1237,1277,1283,1297,1307,1423,1433,1447,1453
%N a(1)=5. For n >= 2, a(n) = the smallest prime p > a(n1) where neither p+1 nor p1 is divisible by any (earlier) term of this sequence.
%C This sequence would have terminated after only one term if a(1) equaled 2 or 3.
%H Robert Israel, <a href="/A166109/b166109.txt">Table of n, a(n) for n = 1..10000</a>
%e a(5) = 37. So we want to look at the primes > 37 to get a(6). 41  1 is divisible by a(1)=5. (And 41+1 is divisible by a(2)=7.) 431 is divisible by a(2)=7. 471 is divisible by a(4)=23. By 531 is not divisible by any earlier terms of the sequence, and 53+1 is not divisible by any earlier terms of the sequence. So a(6) = 53.
%p Res:= 5: S:= 5: p:= 5:
%p count:= 1:
%p while count < 100 do
%p p:= nextprime(p);
%p if igcd((p+1)*(p1),S) = 1 then
%p count:= count+1; Res:= Res, p;
%p S:= S*p;
%p fi
%p od:
%p Res; # _Robert Israel_, Jun 16 2019
%K nonn
%O 1,1
%A _Leroy Quet_, Oct 06 2009
%E Extended by _Ray Chandler_, Mar 12 2010
