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 1-4 of 4 results.

A010514 Decimal expansion of square root of 61.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Comments

Continued fraction expansion is 7 followed by {1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14} repeated. - Harry J. Smith, Jun 07 2009

Examples

			7.810249675906654394129722735759101413568305136648563300177243760190785...

Links

Crossrefs

Cf. A010145 Continued fraction.

Programs

  • Mathematica
    RealDigits[N[61^(1/2),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 22 2012 *)
  • PARI
    { default(realprecision, 20080); x=sqrt(61); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010514.txt", n, " ", d)); } \\ Harry J. Smith, Jun 07 2009

A067280 Number of terms in continued fraction for sqrt(n), excl. 2nd and higher periods.

Original entry on oeis.org

1, 2, 3, 1, 2, 3, 5, 3, 1, 2, 3, 3, 6, 5, 3, 1, 2, 3, 7, 3, 7, 7, 5, 3, 1, 2, 3, 5, 6, 3, 9, 5, 5, 5, 3, 1, 2, 3, 3, 3, 4, 3, 11, 9, 7, 13, 5, 3, 1, 2, 3, 7, 6, 7, 5, 3, 7, 8, 7, 5, 12, 5, 3, 1, 2, 3, 11, 3, 9, 7, 9, 3, 8, 6, 5, 13, 7, 5, 5, 3, 1, 2, 3, 3, 6, 11, 3, 7, 6, 3, 9, 9, 11, 17, 5, 5, 12, 5
Offset: 1

Views

Author

Frank Ellermann, Feb 23 2002

Keywords

Examples

			a(2)=2: [1,(2)+ ]; a(3)=3: [1,(1,2)+ ]; a(4)=1: [2]; a(5)=2: [2,(4)+ ].

References

  • H. Davenport, The Higher Arithmetic. Cambridge Univ. Press, 7th edition, 1999, table 1.

Crossrefs

Related sequences: 2 : A040000, ..., 44: A040037, 48: A040041, ..., 51: A040043, 56: A040048, 60: A040052, 63: A040055, ..., 66: A040057. 68: A040059, 72: A040063, 80: A040071.
Related sequences: 45: A010135, ..., 47: A010137, 52: A010138, ..., 55: A010141, 57: A010142, ..., 59: A010144. 61: A010145, 62: A010146. 67: A010147, 69: A010148, ..., 71: A010150.
Cf. A003285.

Programs

  • Python
    from sympy import continued_fraction_periodic
def A067280(n): return len((a := continued_fraction_periodic(0,1,n))[:1]+(a[1] if a[1:] else [])) # Chai Wah Wu, Jun 14 2022

Formula

a(n) = A003285(n) + 1. - Andrey Zabolotskiy, Jun 23 2020

Extensions

Name clarified by Michel Marcus, Jun 22 2020

A041106 Numerators of continued fraction convergents to sqrt(61).

Original entry on oeis.org

7, 8, 39, 125, 164, 453, 1070, 1523, 5639, 24079, 29718, 440131, 469849, 2319527, 7428430, 9747957, 26924344, 63596645, 90520989, 335159612, 1431159437, 1766319049, 26159626123, 27925945172, 137863406811, 441516165605, 579379572416, 1600275310437
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A010514, A041107, A010145, A020818.

Programs

  • Mathematica
    Numerator[Convergents[Sqrt[61], 30]] (* Vincenzo Librandi, Oct 29 2013 *)

Formula

G.f.: -(x^21 -7*x^20 +8*x^19 -39*x^18 +125*x^17 -164*x^16 +453*x^15 -1070*x^14 +1523*x^13 -5639*x^12 +24079*x^11 +29718*x^10 +24079*x^9 +5639*x^8 +1523*x^7 +1070*x^6 +453*x^5 +164*x^4 +125*x^3 +39*x^2 +8*x +7) / (x^22 +59436*x^11 -1). - Colin Barker, Nov 12 2013

Extensions

More terms from Colin Barker, Nov 12 2013

A041107 Denominators of continued fraction convergents to sqrt(61).

Original entry on oeis.org

1, 1, 5, 16, 21, 58, 137, 195, 722, 3083, 3805, 56353, 60158, 296985, 951113, 1248098, 3447309, 8142716, 11590025, 42912791, 183241189, 226153980, 3349396909, 3575550889, 17651600465, 56530352284, 74181952749, 204894257782, 483970468313, 688864726095
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A041106, A010145, A020818, A010514.

Programs

  • Magma
    I:=[1, 1, 5, 16, 21, 58, 137, 195, 722, 3083, 3805, 56353, 60158, 296985, 951113, 1248098, 3447309, 8142716, 11590025, 42912791, 183241189, 226153980]; [n le 22 select I[n] else 59436*Self(n-11)+Self(n-22): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013
  • Mathematica
    Denominator[Convergents[Sqrt[61], 30]] (* Vincenzo Librandi, Dec 11 2013 *)

Formula

G.f.: -(x^20 -x^19 +5*x^18 -16*x^17 +21*x^16 -58*x^15 +137*x^14 -195*x^13 +722*x^12 -3083*x^11 +3805*x^10 +3083*x^9 +722*x^8 +195*x^7 +137*x^6 +58*x^5 +21*x^4 +16*x^3 +5*x^2 +x +1) / (x^22 +59436*x^11 -1). - Colin Barker, Nov 12 2013
a(n) = 59436*a(n-11) + a(n-22). - Vincenzo Librandi, Dec 11 2013

Extensions

More terms from Colin Barker, Nov 12 2013
Showing 1-4 of 4 results.

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

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