A031713 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 35.

1227, 4904, 11031, 19608, 30635, 44112, 60039, 78416, 99243, 122520, 148247, 176424, 207051, 240128, 275655, 313632, 354059, 396936, 442263, 490040, 540267, 592944, 648071, 705648, 765675, 828152, 893079, 960456, 1030283, 1102560

Offset

1,1

Comments

The continued fraction expansion of sqrt((k*m)^2+t*m) for m >= 1 where t divides 2*k has the form [k*m, 2*k/t, 2*k*m, 2*k/t, 2*k*m, ...]. Thus numbers of the form (35*m)^2 + 2*m for m >= 1 are in the sequence. Are there any others? - Chai Wah Wu, Jun 18 2016

The term 1545120 is not of the form (35*m)^2 + 2*m. - Chai Wah Wu, Jun 19 2016

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Prog

(Python)
from sympy import continued_fraction_periodic
A031713_list = [n for n, d in ((n, continued_fraction_periodic(0, 1, n)[-1]) for n in range(1, 10**5)) if isinstance(d, list) and min(d) == 35] # Chai Wah Wu, Jun 10 2017

Crossrefs

Sequence in context: A031748 A031658 A031533 * A259998 A046958 A032348

Adjacent sequences: A031710 A031711 A031712 * A031714 A031715 A031716

Keyword

nonn

Author

David W. Wilson

Status

approved