cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A031697 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 19.

Original entry on oeis.org

363, 1448, 3255, 5784, 9035, 13008, 17703, 23120, 29259, 36120, 43703, 52008, 61035, 70784, 81255, 92448, 104363, 117000, 130359, 137680, 144440, 152920, 159243, 174768, 191015, 207984, 225675, 244088, 263223, 283080, 303659, 314780, 324960
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

(19*m)^2 + 2*m for m >= 1 are terms of this sequence (see comment in A031749). The first term that is not of this form is a(20) = 137680. - Chai Wah Wu, Jun 19 2016

Links

Programs

  • Mathematica
    Select[Range[350000],!IntegerQ[Sqrt[#]] &&Min[ContinuedFraction[Sqrt[#]][[2]]] == 19&](* Vincenzo Librandi, Feb 10 2012 *)

A031769 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 91.

Original entry on oeis.org

8283, 33128, 74535, 132504, 207035, 298128, 405783, 530000, 670779, 828120, 1002023, 1192488, 1399515, 1623104, 1863255, 2119968, 2393243, 2683080, 2989479, 3312440, 3651963, 4008048, 4380695, 4769904, 5175675, 5598008, 6036903, 6492360
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

(91*m)^2+2*m for m >= 1 is a proper subsequence. It is a subsequence (see comment in A031749) and the term 69339112 is not of this form. - Chai Wah Wu, Jun 19 2016

Links

Programs

  • Mathematica
    cf91Q[n_]:=Module[{s=Sqrt[n]},If[IntegerQ[s],1,Min[ContinuedFraction[s][[2]]]]==91]; Select[Range[65*10^5],cf91Q] (* Harvey P. Dale, Oct 08 2016 *)

A031771 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 93.

Original entry on oeis.org

8651, 34600, 77847, 138392, 216235, 311376, 423815, 553552, 700587, 864920, 1046551, 1245480, 1461707, 1695232, 1946055, 2214176, 2499595, 2802312, 3122327, 3459640, 3814251, 4186160, 4575367, 4981872, 5405675, 5846776, 6305175, 6780872
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

(93*m)^2+2*m for m >= 1 is a proper subsequence. It is a subsequence (see comment in A031749) and the term 75620603 is not of this form. - Chai Wah Wu, Jun 19 2016

Links

Programs

  • Mathematica
    cf93Q[n_]:=Module[{s=Sqrt[n]},If[IntegerQ[s],1,Min[ContinuedFraction[s][[2]]]] == 93]; Select[Range[6781000],cf93Q] (* Harvey P. Dale, Aug 08 2021 *)

A031773 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 95.

Original entry on oeis.org

9027, 36104, 81231, 144408, 225635, 324912, 442239, 577616, 731043, 902520, 1092047, 1299624, 1525251, 1768928, 2030655, 2310432, 2608259, 2924136, 3258063, 3610040, 3980067, 4368144, 4774271, 5198448, 5640675, 6100952, 6579279, 7075656
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

(95*m)^2+2*m for m >= 1 is a proper subsequence. It is a subsequence (see comment in A031749) and the term 82319520 is not of this form. - Chai Wah Wu, Jun 19 2016

Links

A031775 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 97.

Original entry on oeis.org

9411, 37640, 84687, 150552, 235235, 338736, 461055, 602192, 762147, 940920, 1138511, 1354920, 1590147, 1844192, 2117055, 2408736, 2719235, 3048552, 3396687, 3763640, 4149411, 4554000, 4977407, 5419632, 5880675, 6360536, 6859215, 7376712
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

(97*m)^2+2*m for m >= 1 are terms of the sequence (see comment in A031749). The term 89453959 is not of this form. - Chai Wah Wu, Jun 19 2016

Links

Programs

  • Mathematica
    cf97Q[n_]:=Module[{s=Sqrt[n]},If[IntegerQ[s],1,Min[ContinuedFraction[s][[2]]]]==97]; Select[Range[738*10^4],cf97Q] (* Harvey P. Dale, Nov 20 2018 *)
  • Python
    from sympy import continued_fraction_periodic
A031775_list = [n for n, d in ((n, continued_fraction_periodic(0,1,n)[-1]) for n in range(1,10**5)) if isinstance(d, list) and min(d) == 97] # Chai Wah Wu, Jun 10 2017

A031777 Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 99.

Original entry on oeis.org

9803, 39208, 88215, 156824, 245035, 352848, 480263, 627280, 793899, 980120, 1185943, 1411368, 1656395, 1921024, 2205255, 2509088, 2832523, 3175560, 3538199, 3920440, 4322283, 4743728, 5184775, 5645424, 6125675, 6625528, 7144983, 7684040
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

(99*m)^2+2*m for m >= 1 is a proper subsequence (it is a subsequence, see comment in A031749) as the term 97042400 is not of this form. - Chai Wah Wu, Jun 19 2016

Links

Programs

  • Mathematica
    lt99Q[n_]:=Module[{s=Sqrt[n],lt},If[IntegerQ[s],lt=1,lt= Min[ ContinuedFraction[ s][[2]]]];lt==99]; Select[Range[8000000],lt99Q] (* Harvey P. Dale, Apr 20 2013 *)
  • Python
    from sympy import continued_fraction_periodic
A031777_list = [n for n, d in ((n, continued_fraction_periodic(0,1,n)[-1]) for n in range(1,10**5)) if isinstance(d, list) and min(d) == 99] # Chai Wah Wu, Jun 10 2017
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.