A031766 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 88.

1937, 7746, 17427, 30980, 48405, 69702, 94871, 123912, 156825, 193610, 234267, 278796, 327197, 379470, 435615, 495632, 559521, 627282, 698915, 774420, 853797, 937046, 1024167, 1115160, 1210025, 1308762, 1411371, 1517852, 1628205, 1742430

Offset

1,1

Comments

From Chai Wah Wu, Nov 07 2016: (Start)

If r is even, then the least term of the continued fraction of (r*m/2)^2+m is r for all m >= 1. On the other hand, the least term of the continued fraction of r^4/4 + r^3 + 2r^2 + 3r+2 is also r but it is not of the form (r*m/2)^2+m.

If r is odd, then the least term of the continued fraction of (r*m)^2+2m is r for all m >= 1 and the least term of the continued fraction of r^4 + r^3 + 5*(r+1)^2/4 is also r but it is not of the form (r*m)^2+2m.

This means that 1936*m^2 + m are terms of the sequence for all m >= 1 and 15689610 is also a term but not of the form 1936*m^2 + m.

(End)

Links

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

Crossrefs

Sequence in context: A188369 A185570 A367679 * A031542 A214478 A259513

Adjacent sequences: A031763 A031764 A031765 * A031767 A031768 A031769

Keyword

nonn

Author

David W. Wilson

Status

approved