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.

A248258 Egyptian fraction representation of sqrt(31) (A010486) using a greedy function.

Original entry on oeis.org

5, 2, 15, 911, 756131657, 1046059081493109619, 1823555845900657755132295578770597587, 5295210870312939233563525303202129576974975306672437715711158044936692625
Offset: 0

Views

Author

Robert G. Wilson v, Oct 04 2014

Keywords

Crossrefs

Egyptian fraction representations of the square roots: A006487, A224231, A248235-A248322.
Egyptian fraction representations of the cube roots: A129702, A132480-A132574.

Programs

  • Mathematica
    Egyptian[nbr_] := Block[{lst = {IntegerPart[nbr]}, cons = N[ FractionalPart[ nbr], 2^20], denom, iter = 8}, While[
iter > 0, denom = Ceiling[ 1/cons]; AppendTo[ lst, denom]; cons -= 1/denom; iter--]; lst]; Egyptian[ Sqrt[ 31]]

A010129 Continued fraction for sqrt(31).

Original entry on oeis.org

5, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3, 1, 1, 10, 1, 1, 3, 5, 3
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			5.567764362830021922119471298... = 5 + 1/(1 + 1/(1 + 1/(3 + 1/(5 + ...)))). - _Harry J. Smith_, Jun 04 2009

References

  • James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.

Links

Crossrefs

Cf. A010486 (decimal expansion).

Programs

  • Mathematica
    ContinuedFraction[Sqrt[31],300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)
PadRight[{5},120,{10,1,1,3,5,3,1,1}] (* Harvey P. Dale, Jan 10 2025 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(31)); for (n=0, 20000, write("b010129.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

Formula

G.f.: (5 + x + x^2 + 3*x^3 + 5*x^4 + 3*x^5 + x^6 + x^7 + 5*x^8)/(1 - x^8). - Stefano Spezia, Jul 26 2025

A041050 Numerators of continued fraction convergents to sqrt(31).

Original entry on oeis.org

5, 6, 11, 39, 206, 657, 863, 1520, 16063, 17583, 33646, 118521, 626251, 1997274, 2623525, 4620799, 48831515, 53452314, 102283829, 360303801, 1903802834, 6071712303, 7975515137, 14047227440, 148447789537
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041051, A010486.

Programs

Formula

G.f.: -(x^15 -5*x^14 +6*x^13 -11*x^12 +39*x^11 -206*x^10 +657*x^9 -863*x^8 -1520*x^7 -863*x^6 -657*x^5 -206*x^4 -39*x^3 -11*x^2 -6*x -5) / (x^16 -3040*x^8 +1). - Colin Barker, Nov 04 2013

A041051 Denominators of continued fraction convergents to sqrt(31).

Original entry on oeis.org

1, 1, 2, 7, 37, 118, 155, 273, 2885, 3158, 6043, 21287, 112478, 358721, 471199, 829920, 8770399, 9600319, 18370718, 64712473, 341933083, 1090511722, 1432444805, 2522956527, 26662010075, 29184966602, 55846976677, 196725896633, 1039476459842, 3315155276159
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041050, A010129, A020788, A010486.

Programs

  • Magma
    I:=[1, 1, 2, 7, 37, 118, 155, 273, 2885, 3158, 6043, 21287, 112478, 358721, 471199, 829920]; [n le 16 select I[n] else 3040*Self(n-8) - Self(n-16): n in [1..50]]; // Vincenzo Librandi, Dec 10 2013
  • Mathematica
    Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[31],n]]],{n,1,50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011*)
Denominator[Convergents[Sqrt[31], 30]] (* Vincenzo Librandi, Dec 10 2013 *)

Formula

G.f.: -(x^14 -x^13 +2*x^12 -7*x^11 +37*x^10 -118*x^9 +155*x^8 -273*x^7 -155*x^6 -118*x^5 -37*x^4 -7*x^3 -2*x^2 -x -1) / (x^16 -3040*x^8 +1). - Colin Barker, Nov 12 2013

Extensions

More terms from Colin Barker, Nov 12 2013

A177016 Decimal expansion of sqrt(16926).

Original entry on oeis.org

1, 3, 0, 0, 9, 9, 9, 6, 1, 5, 6, 8, 0, 1, 8, 9, 1, 9, 9, 9, 5, 5, 0, 4, 4, 8, 1, 8, 4, 6, 6, 1, 8, 9, 9, 6, 0, 3, 7, 3, 1, 4, 4, 7, 2, 1, 9, 7, 7, 7, 9, 2, 5, 0, 1, 0, 9, 9, 3, 8, 2, 6, 2, 3, 7, 4, 0, 2, 1, 2, 0, 6, 1, 0, 3, 6, 4, 2, 4, 9, 7, 8, 1, 6, 2, 1, 9, 4, 5, 4, 0, 5, 2, 9, 1, 4, 6, 9, 6, 4, 9, 0, 4, 1, 8
Offset: 3

Views

Author

Klaus Brockhaus, May 01 2010

Keywords

Comments

Continued fraction expansion of sqrt(16926) is 130 followed by (repeat 10, 260).
sqrt(16926) = sqrt(2)*sqrt(3)*sqrt(7)*sqrt(13)*sqrt(31).

Examples

			sqrt(16926) = 130.09996156801891999550...

Crossrefs

Cf. A002193 (decimal expansion of sqrt(2)), A002194 (decimal expansion of sqrt(3)), A010465 (decimal expansion of sqrt(7)), A010470 (decimal expansion of sqrt(13)), A010486 (decimal expansion of sqrt(31)), A177015 (decimal expansion of (124+sqrt(16926))/25).

A177035 Decimal expansion of sqrt(13493990).

Original entry on oeis.org

3, 6, 7, 3, 4, 1, 6, 6, 6, 5, 7, 2, 1, 4, 3, 7, 0, 5, 1, 3, 6, 6, 9, 3, 6, 1, 5, 1, 9, 2, 0, 9, 7, 7, 4, 5, 9, 8, 4, 5, 4, 1, 6, 4, 1, 0, 5, 9, 3, 4, 2, 3, 5, 3, 2, 4, 9, 6, 8, 0, 7, 4, 3, 0, 1, 6, 2, 4, 1, 9, 7, 3, 8, 8, 0, 7, 0, 9, 6, 9, 5, 4, 7, 0, 3, 5, 4, 9, 9, 2, 6, 8, 7, 7, 3, 9, 0, 7, 4, 2, 8, 7, 9, 9, 2
Offset: 4

Views

Author

Klaus Brockhaus, May 01 2010

Keywords

Comments

Continued fraction expansion of sqrt(13493990) is 3673 followed by (repeat 2, 2, 2, 7346).
sqrt(13493990) = sqrt(2)*sqrt(5)*sqrt(19)*sqrt(29)*sqrt(31)*sqrt(79).

Examples

			sqrt(13493990) = 3673.41666572143705136693...

Crossrefs

Cf. A002193 (decimal expansion of sqrt(2)), A002163 (decimal expansion of sqrt(5)), A010475 (decimal expansion of sqrt(19)), A010484 (decimal expansion of sqrt(29)), A010486 (decimal expansion of sqrt(31)), A010531 (decimal expansion of sqrt(79)), A177034 (decimal expansion of (9280+3*sqrt(13493990))/14165).

Programs

  • Mathematica
    RealDigits[Sqrt[13493990],10,120][[1]] (* Harvey P. Dale, Nov 11 2016 *)
Showing 1-6 of 6 results.

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