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%I #4 Mar 31 2012 20:17:54
%S 3,19,163,1459,17497,52489,87211,135433,139483,1220347,5419387,
%T 6049243,28934011,86093443,227862073,272010961
%N Primes that divide 2^(3^n)+1 for some n.
%C This sequence is a subsequence of A057719.
%C 272010961 is the last term less than 3*10^9. The n for each prime is 0, 2, 4, 5, 7, 8, 3, 4, 5, 9, 7, 7, 8, 16, 6, 4. Some terms from A111974 are in this sequence also: 411782264189299, 116299474006080119380780339, and 84782316550432407028588866403. If p=2*3^k+1 is prime for an even k, then p is in this sequence.
%e 1220347 belongs to the sequence as it is a factor of 2^(3^9)+1 (This is the largest member of the sequence less than 5000000)
%p with(numtheory):L:=3;for p from 5 to 5000000 do if isprime(p) then q:=op(2,ifactors(order(2,p)));if nops(q)=2 then if op(1,op(1,q))=2 and op(2,op(1,q))=1 and op(1,op(2,q))=3 then L:=L,p;fi;fi;fi;od;L;
%t Reap[Do[p=Prime[n]; mo=MultiplicativeOrder[2, p]; If[EvenQ[mo] && IntegerQ[Log[3,mo/2]], Sow[p]], {n, PrimePi[10^7]}]][[2,1]]
%Y Cf. A057719, A136475, A005621, A136473.
%K more,nonn
%O 1,1
%A _Christopher J. Smyth_, Feb 16 2008
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