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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A274102 a(n) = nearest integer to k*sin(sqrt(k)+j*Pi) where n = 2*k+j, j=0 or 1.

Original entry on oeis.org

0, 0, 1, -1, 2, -2, 3, -3, 4, -4, 4, -4, 4, -4, 3, -3, 2, -2, 1, -1, 0, 0, -2, 2, -4, 4, -6, 6, -8, 8, -10, 10, -12, 12, -14, 14, -16, 16, -18, 18, -19, 19, -21, 21, -22, 22, -23, 23, -24, 24, -24, 24, -24, 24, -24, 24, -23, 23, -23, 23, -22, 22, -20, 20, -19, 19, -17, 17, -15, 15, -13, 13, -10, 10, -7
Offset: 0

Views

Author

N. J. A. Sloane, Jun 11 2016

Keywords

Links

Crossrefs

Sequences of the same type: A272695, A274086, A274087, A274088, A274090, A274091, A274092, A274095, A274096, A274097, A274101, A274102.

Programs

  • Maple
    Digits:=50:
ft:=proc(n,t) local k,j;
j:=(n mod t); k:=(n-j)/t;
round(evalf(k*sin(sqrt(k)+j*Pi)));
end;
[seq(ft(n,2),n=0..120)];

Formula

a(2n) = A274095(n), a(2n+1) = -A274095(n). - Chai Wah Wu, Jun 11 2016

Extensions

Definition corrected by N. J. A. Sloane, Jun 20 2016

A307518 Positive integers m where |m*sin(m)| increases to a new record.

Original entry on oeis.org

1, 2, 4, 5, 8, 11, 14, 17, 20, 23, 24, 27, 30, 33, 36, 39, 42, 46, 49, 52, 55, 58, 61, 68, 71, 74, 77, 80, 83, 90, 93, 96, 99, 102, 105, 115, 118, 121, 124, 127, 137, 140, 143, 146, 159, 162, 165, 168, 181, 184, 187, 190, 206, 209, 212, 228, 231, 234, 250, 253
Offset: 1

Views

Author

Alois P. Heinz, Apr 12 2019

Keywords

Examples

			|a(n)*sin(a(n))|_{n=1..5} = 0.8415..., 1.819..., 3.027..., 4.794..., 7.915... .

Links

Crossrefs

First differences give A307558.
Cf. A004112, A265735, A272695.

A358520 Nearest integer to n/sin(n).

Original entry on oeis.org

1, 2, 21, -5, -5, -21, 11, 8, 22, -18, -11, -22, 31, 14, 23, -56, -18, -24, 127, 22, 25, -2486, -27, -27, -189, 34, 28, 103, -44, -30, -77, 58, 33, 64, -82, -36, -57, 128, 40, 54, -258, -46, -52, 2486, 53, 51, 380, -62, -51, -191, 76, 53, 134, -97
Offset: 1

Views

Author

Bence Bernáth, Nov 20 2022

Keywords

Comments

It is also the nearest integer to sinc(x)^(-1) function.

Examples

			For n=3, 3/sin(3) = 21.25..., therefore a(3) = 21.

Links

Crossrefs

Cf. A272695, A051422, A105666.
Cf. A046947 (Values for n where abs(a(n))/n has records).

Programs

  • Mathematica
    Table[Round[n/Sin[n]], {n, 1, 100}]
  • PARI
    a(n) = round(n/sin(n)); \\ Michel Marcus, Nov 20 2022
Previous Showing 11-13 of 13 results.

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

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