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.

A062360 a(n) = floor(e^(n*Pi)).

Original entry on oeis.org

1, 23, 535, 12391, 286751, 6635623, 153552935, 3553321280, 82226315585, 1902773895292, 44031505860632, 1018919543279304, 23578503968558226, 545622913077172100, 12626092124920479897, 292176517015939695007
Offset: 0

Views

Author

Jason Earls, Jul 06 2001

Keywords

References

  • M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 2.

Links

Crossrefs

Cf. A121905 (ceiling).

Programs

  • PARI
    for(n=0,23,print(floor(exp(1)^(n*Pi))))
  • PARI
    { default(realprecision, 200); e=exp(1); for (n=0, 100, write("b062360.txt", n, " ", floor(e^(n*Pi))) ) } \\ Harry J. Smith, Aug 06 2009

A062511 a(n) = round(exp(n * Pi)).

Original entry on oeis.org

1, 23, 535, 12392, 286751, 6635624, 153552935, 3553321281, 82226315586, 1902773895292, 44031505860632, 1018919543279305, 23578503968558226, 545622913077172100, 12626092124920479898, 292176517015939695007
Offset: 0

Views

Author

Jason Earls, Jun 24 2001

Keywords

Links

Crossrefs

Cf. A062360, A121905.

Programs

  • Magma
    C := ComplexField(); [Round(Exp(n*Pi(C))): n in [0..30]]; // G. C. Greubel, Jan 15 2018
  • Mathematica
    Round[Exp[Range[0,20]Pi]] (* Harvey P. Dale, Oct 06 2014 *)
  • PARI
    for(n=0,21,print1(round(exp(n*Pi)), ", "))
  • PARI
    { default(realprecision, 200); for (n=0, 100, write("b062511.txt", n, " ", round(exp(n*Pi))) ) } \\ Harry J. Smith, Aug 08 2009

A347029 a(n) = ceiling(e^(n*(Pi/2))).

Original entry on oeis.org

1, 5, 24, 112, 536, 2576, 12392, 59610, 286752, 1379411, 6635624, 31920520, 153552936, 738662923, 3553321281, 17093171649, 82226315586, 395547831245, 1902773895293, 9153250784395, 44031505860633, 211812562992414, 1018919543279305, 4901489415968643, 23578503968558227
Offset: 0

Views

Author

Gary W. Adamson, Aug 11 2021

Keywords

Comments

Alternative formula for e^(n*Pi/2) is i^(-n*i), where i = sqrt(-1). Substitute 2i for n in each identity, resulting in e^(Pi*i) = -1; Euler's formula.
A121905 is the bisection of the sequence, ceiling(e^(n*Pi)).

Examples

			a(5) = ceiling(e^(5*Pi/2)) = ceiling(i^(-5*i)) = 2576.

Crossrefs

Cf. A121905 (even bisection), A124507 (floor), A042972.

Programs

  • Mathematica
    a[n_]:=Ceiling[Exp[n Pi/2]]; Table[a[n],{n,0,24}] (* Stefano Spezia, Aug 12 2021 *)
  • PARI
    a(n) = ceil(exp(n*Pi/2)); \\ Michel Marcus, Aug 12 2021

Formula

a(n) = ceiling(e^(n*Pi/2)) = ceiling(i^(-n*i)).
Showing 1-3 of 3 results.

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

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