A091448 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A091448

Numbers k such that a1 > a2, where [a0,a1,a2,...] is the simple continued fraction of sqrt(k).

19, 28, 29, 52, 53, 54, 67, 70, 85, 86, 88, 103, 106, 107, 108, 124, 125, 126, 127, 129, 149, 151, 153, 172, 173, 174, 175, 176, 178, 179, 199, 201, 202, 204, 206, 207, 229, 232, 233, 234, 236, 237, 259, 261, 262, 263, 265, 267, 268, 292, 293, 294, 295, 296

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

sqrt(19) = [4;2,1,3,1,2,8,...], for which a1 = 2 > 1 = a2.

MATHEMATICA

Select[Range@300, Quiet[#[[1]]>#[[2]]&[Last@ContinuedFraction[Sqrt@#]]]&] (* Giorgos Kalogeropoulos, Jul 04 2021 *)

PROG

(PARI) for(k=2, 300, my(c=contfrac(sqrt(k))); if(#c>=3&&c[2]>c[3], print1(k, ", "))) \\ Hugo Pfoertner, Jul 04 2021

CROSSREFS