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 1-9 of 9 results.

A248257 Egyptian fraction representation of sqrt(30) (A010485) using a greedy function.

Original entry on oeis.org

5, 3, 7, 967, 1028069, 2298068118217, 5494201416226460930421913, 8921656602209859921713003519980673897631224869075674, 838074105556913621236663949120105672159883231833809533473972526431411898035963444027095791284399338983624
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[ 30]]

A040024 Continued fraction for sqrt(30).

Original entry on oeis.org

5, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2, 10, 2
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Examples

			5.4772255750516611345696978... = 5 + 1/(2 + 1/(10 + 1/(2 + 1/(10 + ...)))). - _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. A010485 (decimal expansion), A010700.

Programs

  • Maple
    Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
  • Mathematica
    ContinuedFraction[Sqrt[30],300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)
  • PARI
    { allocatemem(932245000); default(realprecision, 28000); x=contfrac(sqrt(30)); for (n=0, 20000, write("b040024.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

Formula

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

A041048 Numerators of continued fraction convergents to sqrt(30).

Original entry on oeis.org

5, 11, 115, 241, 2525, 5291, 55435, 116161, 1217045, 2550251, 26719555, 55989361, 586613165, 1229215691, 12878770075, 26986755841, 282746328485, 592479412811, 6207540456595, 13007560326001, 136283143716605, 285573847759211, 2992021621308715, 6269617090376641
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010485, A041049.

Programs

Formula

G.f.: (5+11*x+5*x^2-x^3)/(1-22*x^2+x^4). - Colin Barker, Jan 02 2012
a(n) = 22*a(n-2) - a(n-4). - Wesley Ivan Hurt, Jun 16 2023

Extensions

More terms from Harvey P. Dale, Apr 04 2013

A041049 Denominators of continued fraction convergents to sqrt(30).

Original entry on oeis.org

1, 2, 21, 44, 461, 966, 10121, 21208, 222201, 465610, 4878301, 10222212, 107100421, 224423054, 2351330961, 4927084976, 51622180721, 108171446418, 1133336644901, 2374844736220, 24881784007101
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010485, A040024, A041048 (numerators).

Programs

Formula

G.f.: (1+2*x-x^2)/(1-22*x^2+x^4). [Colin Barker, Jan 02 2012]

A176057 Decimal expansion of (5+sqrt(30))/5.

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, Apr 07 2010

Keywords

Comments

Continued fraction expansion of (5+sqrt(30))/5 is A010700.

Examples

			(5+sqrt(30))/5 = 2.09544511501033222691...

Links

Crossrefs

Cf. A010485 (decimal expansion of sqrt(30)), A010700 (repeat 2, 10).

A176215 Decimal expansion of (10+2*sqrt(30))/5.

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, Apr 12 2010

Keywords

Comments

Continued fraction expansion of (10+2*sqrt(30))/5 is A010710.

Examples

			(10+2*sqrt(30))/5 = 4.19089023002066445382...

Links

Crossrefs

Cf. A010485 (decimal expansion of sqrt(30)), A010710 (repeat 4, 5).

Programs

  • Mathematica
    RealDigits[(10+2Sqrt[30])/5,10,120][[1]] (* Harvey P. Dale, Nov 28 2011 *)

A176319 Decimal expansion of (5+sqrt(30))/2.

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, Apr 15 2010

Keywords

Comments

Continued fraction expansion of (5+sqrt(30))/2 is A010710 preceded by 5.

Examples

			(5+sqrt(30))/2 = 5.23861278752583056728...

Links

Crossrefs

Cf. A010485 (decimal expansion of sqrt(30)), A010710 (repeat 4, 5).

Programs

  • Magma
    SetDefaultRealField(RealField(120)); (5 + Sqrt(30))/2; // G. C. Greubel, Nov 26 2019
  • Maple
    evalf( (5+sqrt(30))/2, 120); # G. C. Greubel, Nov 26 2019
  • Mathematica
    RealDigits[(5+Sqrt[30])/2,10,120][[1]]  (* Harvey P. Dale, Apr 24 2011 *)
  • PARI
    default(realprecision, 120); (5+sqrt(30))/2 \\ G. C. Greubel, Nov 26 2019
  • Sage
    numerical_approx((5+sqrt(30))/2, digits=120) # G. C. Greubel, Nov 26 2019

A176529 Decimal expansion of 5+sqrt(30).

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, Apr 24 2010

Keywords

Comments

Continued fraction expansion of 5+sqrt(30) is A010700 preceded by 10.
a(n) = A010485(n-2) for n > 3.

Examples

			5+sqrt(30) = 10.47722557505166113456...

Crossrefs

Cf. A010485 (decimal expansion of sqrt(30)), A010700 (repeat 2, 10).

Programs

  • Mathematica
    RealDigits[5+Sqrt[30],10,120][[1]]  (* Harvey P. Dale, Mar 31 2011 *)

A378813 Decimal expansion of sqrt(480)/7.

Original entry on oeis.org

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

Views

Author

Stefano Spezia, Dec 08 2024

Keywords

Examples

			3.1298431857438063626112559017188693368728268285599...

References

  • Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.31.4, p. 201.

Crossrefs

Cf. A010485.

Programs

  • Mathematica
    RealDigits[Sqrt[480]/7,10,100][[1]]

Formula

Equals 4*sqrt(30)/7.
Showing 1-9 of 9 results.

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

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