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.

A121381 a(n) = ceiling(n*Pi).

Original entry on oeis.org

0, 4, 7, 10, 13, 16, 19, 22, 26, 29, 32, 35, 38, 41, 44, 48, 51, 54, 57, 60, 63, 66, 70, 73, 76, 79, 82, 85, 88, 92, 95, 98, 101, 104, 107, 110, 114, 117, 120, 123, 126, 129, 132, 136, 139, 142, 145, 148, 151, 154, 158, 161, 164, 167, 170, 173, 176, 180, 183, 186
Offset: 0

Views

Author

Mohammad K. Azarian, Sep 06 2006

Keywords

Links

Crossrefs

Essentially the same as A004084. Cf. A022844, A121854, A121855.

Programs

  • Magma
    [Ceiling(n*Pi): n in [0..50]]; // G. C. Greubel, Oct 28 2017
  • Mathematica
    Table[Ceiling[n Pi], {n, 0, 80}] (* Vincenzo Librandi, Feb 22 2013 *)
  • PARI
    for(n=0,50, print1(ceil(n*Pi), ", ")) \\ G. C. Greubel, Oct 28 2017

A004082 Numbers k such that sin(k-1) <= 0 and sin(k) > 0.

Original entry on oeis.org

1, 7, 13, 19, 26, 32, 38, 44, 51, 57, 63, 70, 76, 82, 88, 95, 101, 107, 114, 120, 126, 132, 139, 145, 151, 158, 164, 170, 176, 183, 189, 195, 202, 208, 214, 220, 227, 233, 239, 246, 252, 258, 264, 271, 277, 283, 290, 296
Offset: 1

Views

Author

Clark Kimberling

Keywords

Comments

Apart from the first term this is also the sequence ceiling(circumference of a circle of radius n) = ceiling(2*Pi*n), n >= 1. - Mohammad K. Azarian, Feb 29 2008, Aug 01 2009
Bisection of A004084. - Michel Marcus, Mar 21 2013

Links

Crossrefs

Cf. A004084, A066643.
For floor(2*Pi*n) see A038130.
See A277690 for another version.

Programs

  • Mathematica
    Join[{1},Transpose[SequencePosition[Table[If[Sin[n]<=0,1,0],{n,300}],{1,0}]][[2]]] (* The program uses the SequencePosition function from Mathematica version 10 *) (* Harvey P. Dale, Apr 12 2016 *)
  • PARI
    lista(m) = {for (i=1, m, if ((sin(i-1)<=0) && (sin(i) > 0), print1(i, ", ")););} \\ Michel Marcus, Mar 21 2013

Formula

a(n) = A038130(n-1) + 1.

A181784 Numerators of a series sum related to a game of chance.

Original entry on oeis.org

1, 1, 4, 22, 140, 969, 7084, 53820, 420732, 3782992, 32389076, 275617830, 2350749914, 20140518790, 173429992350, 1500850805160, 14550277251918, 133009333771170, 1198324107797254
Offset: 0

Views

Author

Robert Munafo, Dec 21 2010

Keywords

Comments

Consider a 1-dimensional random walk from 0 with equal-probability steps of Pi and -1. One way to compute the probability of eventually walking below 0 is as the sum over n of the probabilities of becoming negative after a walk with exactly n steps of Pi (n >= 0) and max(ceiling(n*Pi),1) steps of -1. The total number of walks of such length for a given n is 2^(n+max(ceiling(n*Pi),1)), or 2^(n+A004084(n)) (n >= 1), forming a sequence of denominators, and this sequence gives the numerators, the number of possible sequences of length (n+max(ceiling(n*Pi),1)) drawn from {Pi, -1} such that no partial sum except the total sum is < 0.
See the Munafo web page for complete description.
a(n) diverges from A002293 because Pi is not exactly 3.

Examples

			Numerators of series sum 1/2 + 1/32 + 4/512 + 22/8192 + 140/131072 + ...

Links

Extensions

a(18) from Robert Munafo, Dec 22 2010
Corrected and added links by Robert Munafo, Jan 01 2024

A145004 Values of n at which the number of roots of the function x+n*cos(x) increases.

Original entry on oeis.org

0, 3, 7, 10, 13, 16, 19, 22, 26, 29, 32, 35, 38, 41, 44, 48, 51
Offset: 0

Views

Author

Sébastien Dumortier, Sep 28 2008

Keywords

Examples

			For n=0..2, there is 1 root. For n=3..6, there are 3 roots. For n=7..9, there are 5 roots. etc... So first ranks are 0,3,7,10, ...

Crossrefs

Cf. A121381, A004084.
Showing 1-4 of 4 results.

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

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