A022853 -id:A022853 - cp's OEIS frontend

A135296 A measure of quality (the higher the better) for the approximation to Pi by rationals A022853(n)/n.

7, 3, 2, 2, 3, 6, 112, 7, 3, 2, 2, 3, 6, 56, 8, 3, 2, 2, 3, 5, 37, 8, 3, 2, 2, 3, 5, 28, 9, 4, 2, 2, 3, 5, 22, 10, 4, 2, 2, 2, 5, 18, 11, 4, 2, 2, 2, 4, 16, 12, 4, 2, 2, 2, 4, 14, 14, 4, 2, 2, 2, 4, 12, 16, 4, 2, 2, 2, 4, 11, 18, 5, 2, 2, 2, 4, 10, 22, 5, 3, 2, 2, 4, 9, 28, 5, 3, 2, 2

Offset: 1

Franz Vrabec, Dec 04 2007

			a(7)=112 because [1/|7*Pi-22|] = [1/|-0.0088514|] = [112.976] = 112.

G. C. Greubel, Table of n, a(n) for n = 1..2500

Cf. A022853.

a = {}; For[n = 1, n < 90, n++, AppendTo[a, Floor[1/(If[FractionalPart[n*Pi] > 1/2, Ceiling[n*Pi] - n*Pi, n*Pi - Floor[n*Pi]])]]]; a (* Stefan Steinerberger, Dec 05 2007 *)

a(n) = [1/|n*Pi-A022853(n)|].

More terms from Stefan Steinerberger, Dec 05 2007

A082964 a(n) = round(n/Pi), n divided by Pi rounded to the nearest integer.

Original entry on oeis.org

0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 25

Offset: 0

Cino Hilliard, May 27 2003

			For n = 11, a(11) = (arctan(tan(11))-11)/Pi = -4;
For n = 12, a(12) = (arctan(tan(12))-12)/Pi = -4;
For n = 13, a(13) = (arctan(tan(13))-13)/Pi = -4;
For n = 14, a(14) = (arctan(tan(14))-14)/Pi = -4.

Hugo Pfoertner, Table of n, a(n) for n = 0..10000
Xavier Gordon and Pascal Sebah, Mathematical Constants and Computations
Cino Hilliard, Qfloat BCX arctan(tan(-3)) etc

Cf. A032615, A296357, A000796, A002485, A022853.

PARI
```
a(n) = round (n/Pi)
```

Simplified NAME from Hugo Pfoertner, Jul 20 2023

A092784 a(n) = round(n*(Pi - 2)).

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82

Offset: 1

Jorge Coveiro, Apr 14 2004

Cf. A005843, A022853.

Maple
```
seq(round(n*(Pi-2)), n=1..81);
```

Table[Round[n*(Pi-2)], {n,1,81}] (* Georg Fischer, Sep 01 2021 *)

a(n) = A022853(n) - A005843(n). - Michel Marcus, Sep 01 2021

Definition edited by Georg Fischer, Sep 01 2021

A282498 a(n) = nearest integer to Pi*prime(n).

Original entry on oeis.org

6, 9, 16, 22, 35, 41, 53, 60, 72, 91, 97, 116, 129, 135, 148, 167, 185, 192, 210, 223, 229, 248, 261, 280, 305, 317, 324, 336, 342, 355, 399, 412, 430, 437, 468, 474, 493, 512, 525, 543, 562, 569, 600, 606, 619, 625, 663, 701, 713, 719, 732, 751, 757, 789, 807

Offset: 1

Ahmad J. Masad, Feb 20 2017

nonn

			a(13) = nearest integer to Pi*prime(13) = the nearest integer to (Pi*41) = 128.805298... = 129, so a(13) = 129.

Cf. A000796.

Subsequence of A022853.

Table[Round[Pi Prime@ n], {n, 55}] (* Michael De Vlieger, Feb 20 2017 *)

a(n) = round(Pi*prime(n)); \\ Michel Marcus, Feb 20 2017

cp's OEIS Frontend

A135296 A measure of quality (the higher the better) for the approximation to Pi by rationals A022853(n)/n.

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A082964 a(n) = round(n/Pi), n divided by Pi rounded to the nearest integer.

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A092784 a(n) = round(n*(Pi - 2)).

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A282498 a(n) = nearest integer to Pi*prime(n).

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PARI