A127451 -id:A127451 - cp's OEIS frontend

A127450 Beatty sequence for 1/(e^Pi - Pi^e), complement of A127451.

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 61, 63, 64, 66, 67, 68, 70, 71, 73, 74, 76, 77, 79, 80, 82, 83, 85, 86, 88, 89, 90, 92, 93, 95, 96, 98, 99, 101, 102

Offset: 1

Robert G. Wilson v, Jan 14 2007

Differs from A054386 at term n=122, where A054386(122)=178, A127450(122)=179. - Martin Fuller, May 10 2007

Martin Fuller, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Beatty Sequence.
Index entries for sequences related to Beatty sequences

Cf. A063504, A054386, A059564.

Table[Floor[n/(Exp[Pi] - Pi^E)], {n, 70}]

a(n) = floor(n/(e^Pi - Pi^e))

Definition corrected by N. J. A. Sloane, May 10 2007

A022844 a(n) = floor(n*Pi).

Original entry on oeis.org

0, 3, 6, 9, 12, 15, 18, 21, 25, 28, 31, 34, 37, 40, 43, 47, 50, 53, 56, 59, 62, 65, 69, 72, 75, 78, 81, 84, 87, 91, 94, 97, 100, 103, 106, 109, 113, 116, 119, 122, 125, 128, 131, 135, 138, 141, 144, 147, 150, 153, 157, 160, 163, 166, 169, 172, 175, 179, 182, 185, 188, 191, 194

Offset: 0

Clark Kimberling

nonn

Beatty sequence for Pi.
Differs from A127451 first at a(57). - L. Edson Jeffery, Dec 01 2013
These are the nonnegative integers m satisfying sin(m)*sin(m+1) <= 0. In general, the Beatty sequence of an irrational number r > 1 consists of the numbers m satisfying sin(m*x)*sin((m+1)*x) <= 0, where x = Pi/r. Thus the numbers m satisfying sin(m*x)*sin((m+1)*x) > 0 form the Beatty sequence of r/(1-r). - Clark Kimberling, Aug 21 2014
This can also be stated in terms of the tangent function. These are the nonnegative integers m such that tan(m/2)*tan(m/2+1/2) <= 0. In general, the Beatty sequence of an irrational number r > 1 consists of the numbers m satisfying tan(m*x/2)*tan((m+1)*x/2) <= 0, where x = Pi/r. Thus the numbers m satisfying tan(m*x/2)*tan((m+1)*x/2) > 0 form the Beatty sequence of r/(1-r). - Clark Kimberling, Aug 22 2014

			a(7)=21 because 7*Pi=21.9911... and a(8)=25 because 8*Pi=25.1327.... a(100000)=314159 because Pi=3.141592...

Ivan Panchenko, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Beatty Sequence.
Index entries for sequences related to Beatty sequences

Cf. A000796, A054386, A038130, A108591, A127451, A140758.

First differences give A063438.

R:=RieldField(10); [Floor(n*Pi(R)): n in [0..80]]; // G. C. Greubel, Sep 28 2018

a:=n->floor(n*Pi): seq(a(n),n=0..70); # Muniru A Asiru, Sep 28 2018

Floor[Pi Range[0,200]] (* Harvey P. Dale, Aug 27 2024 *)

vector(80, n, n--; floor(n*Pi)) \\ G. C. Greubel, Sep 28 2018

a(n)/n converges to Pi because |a(n)/n - Pi| = |a(n) - n*Pi|/n < 1/n. - Hieronymus Fischer, Jan 22 2006

Previous Mathematica program replaced by Harvey P. Dale, Aug 27 2024

cp's OEIS Frontend

A127450 Beatty sequence for 1/(e^Pi - Pi^e), complement of A127451.

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