A031712 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 34.

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

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