A031702 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 24.

145, 578, 1299, 2308, 3605, 5190, 7063, 9224, 11673, 14410, 17435, 20748, 24349, 28238, 32415, 36880, 41633, 46674, 52003, 57620, 63525, 69718, 76199, 82968, 90025, 97370, 97994, 105003, 112924, 121133, 129630, 138415, 147488, 156849, 166498

Offset

1,1

Links

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

Example

The continued fraction for sqrt(97994) is 313, [25, 24, 25, 626], where the smallest term of the periodic part is 24, so 97994 belongs to the sequence.

Mathematica

Select[Range[200000], !IntegerQ[Sqrt[#]] && Min[ContinuedFraction[Sqrt[#]][[2]]] == 24&] (* Vincenzo Librandi, Feb 06 2012 *)

Prog

(Python)
from sympy import continued_fraction_periodic
A031702_list = [n for n, s in ((i, continued_fraction_periodic(0, 1, i)[-1]) for i in range(1, 10**5)) if isinstance(s, list) and min(s) == 24] # Chai Wah Wu, Jun 08 2017

Crossrefs

Cf. A031424.

Sequence in context: A207058 A116208 A211470 * A297732 A354669 A296972

Adjacent sequences: A031699 A031700 A031701 * A031703 A031704 A031705

Keyword

nonn

Author

David W. Wilson

Status

approved