A118612 Denominator if the numerator and denominator of the continued fraction rational approximation of sqrt(2) are both prime.

2, 5, 29, 44560482149, 13558774610046711780701

Offset: 1

Author

Joshua Zucker, May 08 2006

Keywords

• frac
• nonn

Comments

Next term, if it exists, is bigger than 489 digits (the 1279th convergent to sqrt(2)).

Links

• Andrej Dujella, Mirela Jukić Bokun, Ivan Soldo, A Pellian equation with primes and applications to D(-1)-quadruples, arXiv:1706.01959 [math.NT], 2017.

Crossrefs

A086397 has the numerators. This sequence is a subsequence of A000129, A086383 and A101411.

Programs

Mathematica

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 *)