A031697 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 19.

363, 1448, 3255, 5784, 9035, 13008, 17703, 23120, 29259, 36120, 43703, 52008, 61035, 70784, 81255, 92448, 104363, 117000, 130359, 137680, 144440, 152920, 159243, 174768, 191015, 207984, 225675, 244088, 263223, 283080, 303659, 314780, 324960

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

(19*m)^2 + 2*m for m >= 1 are terms of this sequence (see comment in A031749). The first term that is not of this form is a(20) = 137680. - Chai Wah Wu, Jun 19 2016

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 60 terms from Vincenzo Librandi)

Programs

Mathematica

Select[Range[350000],!IntegerQ[Sqrt[#]] &&Min[ContinuedFraction[Sqrt[#]][[2]]] == 19&](* Vincenzo Librandi, Feb 10 2012 *)