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%I #10 Nov 22 2017 01:38:13
%S 2,5,29,44560482149,13558774610046711780701
%N Denominator if the numerator and denominator of the continued fraction rational approximation of sqrt(2) are both prime.
%C Next term, if it exists, is bigger than 489 digits (the 1279th convergent to sqrt(2)).
%H Andrej Dujella, Mirela Jukić Bokun, Ivan Soldo, <a href="https://arxiv.org/abs/1706.01959">A Pellian equation with primes and applications to D(-1)-quadruples</a>, arXiv:1706.01959 [math.NT], 2017.
%t For[n = 2, n < 1500, n++, a := Join[{1}, Table[2, {i, 2, n}]]; If[PrimeQ[Denominator[FromContinuedFraction[a]]], If[PrimeQ[Numerator[FromContinuedFraction[a]]], Print[Denominator[FromContinuedFraction[a]]]]]] (* _Stefan Steinerberger_, May 09 2006 *)
%Y A086397 has the numerators. This sequence is a subsequence of A000129, A086383 and A101411.
%K frac,nonn
%O 1,1
%A _Joshua Zucker_, May 08 2006
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