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 1-3 of 3 results.

A176443 Decimal expansion of sqrt(469).

Original entry on oeis.org

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

Views

Author

Klaus Brockhaus, Apr 19 2010

Keywords

Comments

Continued fraction expansion of sqrt(469) is A040447.

Examples

			sqrt(469) = 21.65640782770771520178...

Crossrefs

Cf. A010465 (decimal expansion of sqrt(7)), A010519 (decimal expansion of sqrt(67)), A176442 (decimal expansion of (21+sqrt(469))/6), A040447.

Programs

  • Mathematica
    RealDigits[Sqrt[469],10,120][[1]] (* Harvey P. Dale, May 28 2025 *)

A041894 Numerators of continued fraction convergents to sqrt(469).

Original entry on oeis.org

21, 22, 43, 65, 693, 4223, 42923, 47146, 90069, 137215, 5853099, 5990314, 11843413, 17833727, 190180683, 1158917825, 11779358933, 12938276758, 24717635691, 37655912449, 1606265958549, 1643921870998, 3250187829547, 4894109700545, 52191284834997
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041895, A176443, A040447.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[469], 30]] (* Harvey P. Dale, Mar 28 2013 *)

Formula

G.f.: -(x^19 -21*x^18 +22*x^17 -43*x^16 +65*x^15 -693*x^14 +4223*x^13 -42923*x^12 +47146*x^11 -90069*x^10 -137215*x^9 -90069*x^8 -47146*x^7 -42923*x^6 -4223*x^5 -693*x^4 -65*x^3 -43*x^2 -22*x -21) / (x^20 -274430*x^10 +1). - Colin Barker, Nov 26 2013

Extensions

More terms from Colin Barker, Nov 26 2013

A041895 Denominators of continued fraction convergents to sqrt(469).

Original entry on oeis.org

1, 1, 2, 3, 32, 195, 1982, 2177, 4159, 6336, 270271, 276607, 546878, 823485, 8781728, 53513853, 543920258, 597434111, 1141354369, 1738788480, 74170470529, 75909259009, 150079729538, 225988988547, 2409969615008, 14685806678595, 149268036400958
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041894, A176443, A040447.

Programs

  • Magma
    I:=[1,1,2,3,32,195,1982,2177,4159,6336,270271, 276607,546878,823485,8781728,53513853,543920258, 597434111,1141354369,1738788480]; [n le 20 select I[n] else 274430*Self(n-10)-Self(n-20): n in [1..50]]; // Vincenzo Librandi, Dec 26 2013
  • Mathematica
    Denominator[Convergents[Sqrt[469], 30]] (* Vincenzo Librandi, Dec 26 2013 *)
LinearRecurrence[{0,0,0,0,0,0,0,0,0,274430,0,0,0,0,0,0,0,0,0,-1},{1,1,2,3,32,195,1982,2177,4159,6336,270271,276607,546878,823485,8781728,53513853,543920258,597434111,1141354369,1738788480},30] (* Harvey P. Dale, Mar 23 2023 *)

Formula

G.f.: -(x^18 -x^17 +2*x^16 -3*x^15 +32*x^14 -195*x^13 +1982*x^12 -2177*x^11 +4159*x^10 -6336*x^9 -4159*x^8 -2177*x^7 -1982*x^6 -195*x^5 -32*x^4 -3*x^3 -2*x^2 -x -1) / (x^20 -274430*x^10 +1). - Colin Barker, Nov 26 2013
a(n) = 274430*a(n-10) - a(n-20) for n>19. - Vincenzo Librandi, Dec 26 2013

Extensions

More terms from Colin Barker, Nov 26 2013
Showing 1-3 of 3 results.

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

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