

A031712


Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 34.


3



290, 1158, 2604, 4628, 7230, 10410, 14168, 18504, 23418, 28910, 34980, 41628, 48854, 56658, 65040, 74000, 83538, 93654, 104348, 115620, 127470, 139898, 152904, 166488, 180650, 195390, 210708, 226604, 243078, 260130, 277760, 295968, 314754, 334118, 354060, 374580, 375804
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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 (17*m)^2 + m for m >= 1 are in the sequence. Are there any others?  Chai Wah Wu, Jun 18 2016
The term 375804 is not of the form (17*m)^2 + m.  Chai Wah Wu, Jun 19 2016


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


CROSSREFS

Sequence in context: A158255 A295483 A075299 * A251049 A108881 A186547
Adjacent sequences: A031709 A031710 A031711 * A031713 A031714 A031715


KEYWORD

nonn


AUTHOR

David W. Wilson


EXTENSIONS

a(35)a(37) from Charles R Greathouse IV, Aug 03 2017


STATUS

approved



