login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

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 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A031509 Numbers k such that the continued fraction for sqrt(k) has even period and if the last term of the periodic part is deleted the central term is 11. 2
123, 127, 131, 139, 151, 163, 167, 488, 512, 520, 544, 608, 640, 672, 1095, 1167, 1383, 1455, 1515, 1944, 2008, 2136, 2264, 2456, 2648, 2696, 3035, 3115, 3215, 3235, 3415, 3515, 3635, 3715, 3735, 3835, 3935, 4115, 4135, 4215, 4368, 4944, 5496, 5943, 5971 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..1000

EXAMPLE

The c.f. expansion of sqrt(127) is 11, [3, 1, 2, 2, 7, 11, 7, 2, 2, 1, 3, 22], [3, 1, 2, 2, 7, 11, 7, 2, 2, 1, 3, 22], ... If the 22 is deleted from the periodic part the central term is 11. - N. J. A. Sloane, Aug 17 2021

MAPLE

# Maple 2016 or later.

filter:= proc(n) uses NumberTheory; local R;

  if issqr(n) then return false fi;

  R:= Term(ContinuedFraction(sqrt(n)), periodic)[2];

  nops(R)::even and R[nops(R)/2] = 11

end proc:

select(filter, [$2..10000]); # Robert Israel, Jun 07 2019

MATHEMATICA

okQ[k_] := Module[{c, lc}, If[IntegerQ[Sqrt[k]], False,

     c = ContinuedFraction[Sqrt[k]]; lc = Length[c[[2]]];

     EvenQ[lc] && c[[2, lc/2]] == 11]];

Select[Range[10000], okQ] (* Jean-François Alcover, Jul 09 2021 *)

CROSSREFS

Sequence in context: A192231 A341992 A077378 * A247616 A119426 A138059

Adjacent sequences:  A031506 A031507 A031508 * A031510 A031511 A031512

KEYWORD

nonn

AUTHOR

David W. Wilson

EXTENSIONS

Definitions of A031509-A031598 clarified by N. J. A. Sloane, Aug 17 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 10:19 EST 2021. Contains 349563 sequences. (Running on oeis4.)