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.

A065114 Sum of terms in the period of continued fraction for sqrt(n) (A010340) is a square.

Original entry on oeis.org

5, 11, 24, 29, 31, 34, 39, 41, 56, 61, 65, 79, 88, 97, 104, 114, 136, 146, 151, 153, 168, 218, 230, 264, 269, 281, 287, 306, 311, 325, 391, 424, 445, 447, 459, 466, 482, 491, 494, 509, 522, 560, 563, 579, 586, 624, 637, 659, 667, 698, 712, 714, 716, 731, 791
Offset: 1

Views

Author

Robert G. Wilson v, Nov 12 2001

Keywords

Programs

  • Mathematica
    Do[ If[ !IntegerQ[ Sqrt[n]] && IntegerQ[ Sqrt[ Apply[ Plus, Last[ ContinuedFraction[ Sqrt[ n]]]]]], Print[n]], {n, 1, 1000} ]

A010341 Sum of all terms except last in period of continued fraction for sqrt(n).

Original entry on oeis.org

0, 0, 1, 0, 0, 2, 3, 1, 0, 0, 3, 2, 4, 4, 1, 0, 0, 4, 9, 2, 6, 10, 5, 1, 0, 0, 5, 8, 6, 2, 15, 3, 4, 6, 1, 0, 0, 6, 4, 3, 4, 2, 17, 8, 8, 22, 7, 1, 0, 0, 7, 12, 8, 12, 6, 2, 8, 6, 13, 4
Offset: 1

Views

Author

N. J. A. Sloane, Walter Gilbert

Keywords

Links

Crossrefs

Cf. A010340

Programs

  • Mathematica
    Table[With[{s=Sqrt[n]},If[IntegerQ[s],0,Total[Most[ContinuedFraction[s][[2]]]]]],{n,60}] (* Harvey P. Dale, Jul 20 2025 *)

A031402 Sum of terms in period of continued fraction for sqrt(a(n)) increases.

Original entry on oeis.org

2, 3, 5, 6, 7, 11, 13, 18, 19, 22, 31, 43, 46, 61, 67, 94, 109, 127, 139, 151, 166, 199, 211, 214, 271, 301, 331, 379, 454, 526, 571, 631, 694, 739, 751, 859, 886, 919, 991, 1279, 1291, 1366, 1549, 1579, 1621, 1726, 1831, 1894, 1999, 2011, 2206
Offset: 1

Views

Author

David W. Wilson

Keywords

Comments

Least k such that the sum of terms in period of continued fraction for sqrt(k) exceeds that for all j's < k.

Crossrefs

Cf. A031403, A010340.

Programs

  • Mathematica
    f[n_] := If[IntegerQ[Sqrt[n]], 0, Apply[ Plus, Last[ ContinuedFraction[ Sqrt[n]]]]]; a = 0; Do[ b = f[n]; If[b > a, a = b; Print[n]], {n, 1, 1000} ]

A010212 Continued fraction for sqrt(163).

Original entry on oeis.org

12, 1, 3, 3, 2, 1, 1, 7, 1, 11, 1, 7, 1, 1, 2, 3, 3, 1, 24, 1, 3, 3, 2, 1, 1, 7, 1, 11, 1, 7, 1, 1, 2, 3, 3, 1, 24, 1, 3, 3, 2, 1, 1, 7, 1, 11, 1, 7, 1, 1, 2, 3, 3, 1, 24, 1, 3, 3, 2, 1, 1, 7, 1, 11, 1, 7, 1, 1, 2, 3, 3, 1, 24, 1, 3, 3, 2, 1
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010121, A010340.

Programs

A065098 Sum of reciprocals of terms in period of continued fraction for sqrt(n) is an integer.

Original entry on oeis.org

239, 1839, 24627
Offset: 1

Views

Author

Naohiro Nomoto, Nov 12 2001

Keywords

Comments

No additional terms up to n = 1 million. - Harvey P. Dale, Apr 11 2016

Examples

			For n=239 the quotient periods are: [[15],[2,5,1,2,4,15,4,2,1,5,2,30]], (1/2)+(1/5)+1+(1/2)+(1/4)+(1/15)+(1/4)+(1/2)+1+(1/5)+(1/2)+(1/30) = 5.

Crossrefs

Cf. A003285, A010340.

Programs

  • Mathematica
    Do[ If[ IntegerQ[ Apply[ Plus, 1/Last[ ContinuedFraction[ Sqrt[n]]]]], Print[n]], {n, 2, 10^5 } ]
srcfiQ[n_]:=Module[{s=Sqrt[n]},IntegerQ[If[IntegerQ[s],1/2,Total[1/ ContinuedFraction[s][[2]]]]]]; Select[Range[25000],srcfiQ] (* Harvey P. Dale, Apr 11 2016 *)

A065115 Least k such that the sum of terms in period of continued fraction for sqrt(k) is n.

Original entry on oeis.org

2, 3, 5, 8, 6, 7, 12, 11, 13, 35, 18, 23, 21, 27, 29, 19, 22, 47, 44, 51, 53, 96, 66, 31, 52, 59, 85, 43, 73, 115, 108, 71, 46, 107, 61, 167, 86, 171, 76, 67, 129, 223, 178, 131, 158, 303, 162, 287, 134, 103, 205, 267, 94, 359, 242, 363, 109, 243, 236, 439, 157, 127
Offset: 2

Views

Author

Robert G. Wilson v, Nov 12 2001

Keywords

Crossrefs

Cf. A010340.

Programs

  • Mathematica
    a = Table[0, {100} ]; Do[ If[ a[[f[n]]] == 0, a[[f[n]]] = n], {n, 101, 1000} ]; a
Showing 1-6 of 6 results.

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

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