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 1-5 of 5 results.

A063503 Continued fraction for e^Pi - Pi^e (A063504 = A039661 - A059850).

Original entry on oeis.org

0, 1, 2, 7, 7, 6, 2, 1, 6, 2, 5, 7, 1, 3, 1, 1, 6, 1, 1, 1, 1, 1, 2, 1, 11, 5, 6, 2, 1, 124, 1, 4, 2, 1, 1, 3, 18, 1, 1, 1, 1, 17, 1, 2, 10, 1, 1, 1, 2, 2, 2, 2, 3, 1, 2, 4, 84, 1, 1, 1, 4, 1, 1, 15, 2, 1, 1, 17, 1, 1, 8, 1, 1, 10, 1, 3, 1, 2, 2, 1, 2, 1, 2, 4, 22, 4, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 2, 9
Offset: 0

Views

Author

Robert G. Wilson v, Jul 30 2001

Keywords

Examples

			0.6815349144182235323019341634048123526710...
		

Crossrefs

Cf. A063504 (decimal expansion).

Programs

  • Mathematica
    ContinuedFraction[E^Pi - Pi^E, 100]
  • PARI
    { allocatemem(932245000); default(realprecision, 21000); e=exp(1); x=contfrac(e^Pi - Pi^e); for (n=1, 20000, write("b063503.txt", n-1, " ", x[n])) } \\ Harry J. Smith, Aug 24 2009

Extensions

Offset changed by Andrew Howroyd, Aug 04 2024

A064441 Increasing partial quotients of e^Pi - Pi^e (A063504).

Original entry on oeis.org

1, 2, 7, 11, 124, 146, 205, 1121, 2101, 3333, 20899, 45415, 54103, 67629, 148987, 319183, 757657
Offset: 1

Views

Author

Robert G. Wilson v, Oct 01 2001

Keywords

Crossrefs

Cf. A063503 (continued fraction).

Programs

  • Mathematica
    t1 = ContinuedFraction[ N[ E^Pi - Pi^E, 9.8 10^5], 952040]; a = 0; Do[ If[ t1[[n]] > a, a = t1[[n]]; Print[a]], {n, 1, 952040} ]

A121930 a(n) = floor(n*(e^Pi - Pi^e)).

Original entry on oeis.org

0, 0, 1, 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 31, 32, 32, 33, 34, 34, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 44, 44, 45, 46, 47, 47, 48, 49, 49
Offset: 0

Views

Author

Mohammad K. Azarian, Sep 02 2006

Keywords

Comments

Beatty sequence of A063504. - R. J. Mathar, Aug 11 2012

Crossrefs

Programs

  • Magma
    C := ComplexField(); [Floor(n*(Exp(1)^Pi(C) - Pi(C)^Exp(1) )): n in [0..50]]; // G. C. Greubel, Nov 06 2017
  • Mathematica
    With[{c=E^Pi-Pi^E},Floor[c*Range[0,80]]] (* Harvey P. Dale, Jan 06 2012 *)
  • PARI
    for(n=0,50, print1(floor(n*(exp(Pi) - Pi^exp(1))), ", ")) \\ G. C. Greubel, Nov 06 2017
    

A127450 Beatty sequence for 1/(e^Pi - Pi^e), complement of A127451.

Original entry on oeis.org

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 63, 64, 66, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 90, 92, 93, 95, 96, 98, 99, 101, 102
Offset: 1

Author

Robert G. Wilson v, Jan 14 2007

Keywords

Comments

Differs from A054386 at term n=122, where A054386(122)=178, A127450(122)=179. - Martin Fuller, May 10 2007

Crossrefs

Programs

  • Mathematica
    Table[Floor[n/(Exp[Pi] - Pi^E)], {n, 70}]

Formula

a(n) = floor(n/(e^Pi - Pi^e))

Extensions

Definition corrected by N. J. A. Sloane, May 10 2007

A127451 Beatty sequence for 1/(1 - e^Pi + Pi^e), complement of A127450.

Original entry on oeis.org

3, 6, 9, 12, 15, 18, 21, 25, 28, 31, 34, 37, 40, 43, 47, 50, 53, 56, 59, 62, 65, 69, 72, 75, 78, 81, 84, 87, 91, 94, 97, 100, 103, 106, 109, 113, 116, 119, 122, 125, 128, 131, 135, 138, 141, 144, 147, 150, 153, 157, 160, 163, 166, 169, 172, 175, 178, 182, 185, 188
Offset: 1

Author

Robert G. Wilson v, Jan 14 2007

Keywords

Comments

Differs from A022844 first at a(57). - L. Edson Jeffery, Dec 01 2013
1/(1 - e^Pi + Pi^e) = 3.140061643.., so a(n)<=A022844(n). - R. J. Mathar, May 30 2025

Crossrefs

Programs

  • Mathematica
    Table[Floor[n/(1 - Exp[Pi] + Pi^E)], {n, 60}]

Formula

a(n) = floor(n/(1 - e^Pi + Pi^e))
Showing 1-5 of 5 results.