

A031713


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


1



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
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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



