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.

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A286307 a(n) is the numerator of r(n), where r(n) = r(n-1) + r(n-2)/(2*(n-1)) with r(0) = 0, r(1) = 1.

Original entry on oeis.org

0, 1, 1, 5, 17, 151, 823, 10631, 15871, 1344097, 12731713, 266731133, 3061359593, 15281334539, 1030023060151, 29833932429263, 461929309281059, 15229246883432833, 53257613193371021, 9845267571825141941, 191853269052081088769, 462422990938113014567, 168922073145947967975799
Offset: 0

Views

Author

Terry D. Grant, May 05 2017

Keywords

Links

Crossrefs

Cf. A019609, A268363, A287596 (denominators).

Programs

  • Maple
    R[0]:= 0: R[1]:= 1: A[0]:= 0: A[1]:= 1:
for n from 2 to 30 do
  R[n]:= R[n-1] + R[n-2]/(2*(n-1));
  A[n]:= numer(R[n]);
od:
seq(A[i],i=0..30); # Robert Israel, May 25 2017
  • Mathematica
    Numerator[RecurrenceTable[{r[n] == r[n - 1] + r[n - 2]/(2 (n - 1)), r[0] == 0, r[1] == 1}, r, {n, 0, 25}]]
  • PARI
    a(n) = if(n < 2, return(n)); n++; my(v=vector(n)); v[1]=0; v[2] = 1; for(i = 3, n, v[i] = v[i-1] + v[i-2]/(2*i - 4)); numerator(v[#v]) \\ David A. Corneth, May 14 2017

Formula

From Wolfdieter Lang, Jun 07 2017: (Start)
G.f. of {r(n)}_{n>=0}: x*exp(-x/2)/(1-x)^(3/2).
a(n) = numerator(r(n)). See the name for the recurrence of r(n). (End)

Extensions

Name changed, a(0) and a(1) added by David A. Corneth, May 14 2017
a(20)-a(22) from David A. Corneth, May 21 2017
Name corrected by Robert Israel, May 25 2017

A291854 Decimal expansion of the "Pi AND e" (Piande) constant.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Sep 13 2017

Keywords

Comments

Pi_2 = 11.00100100001111110... -> 3.1415926535897...
e_2 = 10.10110111111000010... -> 2.7182818284590...
Pi_2 AND e_2 = 10.00100100001000010... -> 2.1411323548533...

Examples

			2.1411323548533155483334288212398570571182864149673143672536880794...

Crossrefs

Cf. A000796, A001113, A004593, A004601, A019609, A059742, A114916, A228239, A231325, A292101, A292107, A291858.

Formula

Equals A059742 - A291858 = A291858 - A114916.

A291858 Decimal expansion of the "Pi OR e" (Piore) constant.

Original entry on oeis.org

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

Views

Author

Alois P. Heinz, Sep 13 2017

Keywords

Comments

Pi_2 = 11.00100100001111110... -> 3.1415926535897...
e_2 = 10.10110111111000010... -> 2.7182818284590...
Pi_2 OR e_2 = 11.10110111111111110... -> 3.7187421271955...

Examples

			3.71874212719552292548950203339230832483613007810775102868822414063...

Crossrefs

Cf. A000796, A001113, A004593, A004601, A019609, A059742, A114916, A228239, A231325, A292101, A292107, A291854.

Formula

Equals A059742 - A291854 = A291854 + A114916.

A019624 Decimal expansion of Pi*e/16.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A019609 (Pi*e).

Programs

  • Magma
    C := ComplexField(); Pi(C)*Exp(1)/16; // G. C. Greubel, Jan 28 2018
  • Mathematica
    RealDigits[Pi*E/16, 10, 50][[1]] (* G. C. Greubel, Jan 28 2018 *)
  • PARI
    Pi*exp(1)/16 \\ G. C. Greubel, Jan 28 2018

A019625 Decimal expansion of Pi*e/17.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A019609 (Pi*e).

Programs

  • Magma
    C := ComplexField(); Pi(C)*Exp(1)/17; // G. C. Greubel, Jan 28 2018
  • Mathematica
    RealDigits[Pi*E/17, 10, 50][[1]] (* G. C. Greubel, Jan 28 2018 *)
  • PARI
    Pi*exp(1)/17 \\ G. C. Greubel, Jan 28 2018

A019626 Decimal expansion of Pi*e/18.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A019609 (Pi*e).

Programs

  • Magma
    C := ComplexField(); Pi(C)*Exp(1)/18; // G. C. Greubel, Jan 28 2018
  • Mathematica
    RealDigits[Pi*E/18, 10, 50][[1]] (* G. C. Greubel, Jan 28 2018 *)
  • PARI
    Pi*exp(1)/18 \\ G. C. Greubel, Jan 28 2018

A019627 Decimal expansion of Pi*e/19.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A019609 (e*Pi).

Programs

  • Magma
    C := ComplexField(); Pi(C)*Exp(1)/19; // G. C. Greubel, Jan 28 2018
  • Mathematica
    RealDigits[Pi*E/19, 10, 50][[1]] (* G. C. Greubel, Jan 28 2018 *)
  • PARI
    Pi*exp(1)/19 \\ G. C. Greubel, Jan 28 2018

A019629 Decimal expansion of Pi*e/21.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A019609 (e*Pi).

Programs

  • Magma
    C := ComplexField(); Pi(C)*Exp(1)/21; // G. C. Greubel, Jan 28 2018
  • Mathematica
    RealDigits[Pi*E/21, 10, 50][[1]] (* G. C. Greubel, Jan 28 2018 *)
  • PARI
    Pi*exp(1)/21 \\ G. C. Greubel, Jan 28 2018

A019630 Decimal expansion of Pi*e/22.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Examples

			0.3881697373942530484301614031612079315924949334438688619...

Links

Crossrefs

Cf. A019609 (Pi*e).

Programs

  • Magma
    C := ComplexField(); Pi(C)*Exp(1)/22; // G. C. Greubel, Jan 28 2018
  • Mathematica
    RealDigits[Pi*E/22, 10, 50][[1]] (* G. C. Greubel, Jan 28 2018 *)
  • PARI
    Pi*exp(1)/22 \\ G. C. Greubel, Jan 28 2018

A019631 Decimal expansion of Pi*e/23.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane

Keywords

Examples

			0.371292792290155089802763081284633673697169...

Links

Crossrefs

Cf. A019609 (e*Pi).

Programs

  • Magma
    C := ComplexField(); Pi(C)*Exp(1)/23; // G. C. Greubel, Jan 28 2018
  • Mathematica
    RealDigits[(Pi E)/23,10,120][[1]] (* Harvey P. Dale, May 10 2012 *)
  • PARI
    Pi*exp(1)/23 \\ G. C. Greubel, Jan 28 2018
Previous Showing 11-20 of 41 results. Next

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

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