A108599 -id:A108599 - cp's OEIS frontend

A022843 Beatty sequence for e: a(n) = floor(n*e).

0, 2, 5, 8, 10, 13, 16, 19, 21, 24, 27, 29, 32, 35, 38, 40, 43, 46, 48, 51, 54, 57, 59, 62, 65, 67, 70, 73, 76, 78, 81, 84, 86, 89, 92, 95, 97, 100, 103, 106, 108, 111, 114, 116, 119, 122, 125, 127, 130, 133, 135, 138, 141, 144, 146, 149, 152, 154, 157, 160

Offset: 0

Clark Kimberling

nonn

a(n) <= A022852(n) <= A121384(n). - Reinhard Zumkeller, Mar 17 2015

Reinhard Zumkeller, 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. A054385, A108599.

Cf. A001113 (e), A022852, A121384.

a022843 n = a022843_list !! n
a022843_list = map (floor . (* e) . fromIntegral) [0..] where e = exp 1
-- Reinhard Zumkeller, Jul 06 2013

[Floor(n*Exp(1)): n in [0..60]]; // G. C. Greubel, Sep 28 2018

A022843 := proc(n)
    floor(n*exp(1)) ;
end proc: # R. J. Mathar, Jan 25 2015

Mathematica
```
Table[ Floor[n*E], {n, 1, 61}]
```

for (n=0, 100, print1(floor(n*exp(1)),", ")) \\ Indranil Ghosh, Mar 21 2017

import math
from mpmath import mp, e
mp.dps = 100
print([int(math.floor(n*e)) for n in range(51)]) # Indranil Ghosh, Mar 21 2017

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

A054385 Beatty sequence for e/(e-1); complement of A022843.

Original entry on oeis.org

1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 17, 18, 20, 22, 23, 25, 26, 28, 30, 31, 33, 34, 36, 37, 39, 41, 42, 44, 45, 47, 49, 50, 52, 53, 55, 56, 58, 60, 61, 63, 64, 66, 68, 69, 71, 72, 74, 75, 77, 79, 80, 82, 83, 85, 87, 88, 90, 91, 93, 94, 96, 98, 99, 101, 102, 104, 105, 107, 109

Offset: 1

Eric W. Weisstein

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Beatty Sequence
Index entries for sequences related to Beatty sequences

Cf. A022843.

Cf. A108599.

a054385 n = a054385_list !! n
a054385_list = map (floor . (* e') . fromIntegral) [1..]
   where e' = e / (e - 1); e = exp 1
-- Reinhard Zumkeller, Jul 06 2013

A054385 := proc(n)
    floor(n*exp(1)/(exp(1)-1)) ;
end proc: # R. J. Mathar, Jan 25 2015

a[n_] := Floor[n E/(E - 1)];
Array[a, 100] (* Jean-François Alcover, Mar 24 2020 *)

from sympy import E
print([n*E//(E-1) for n in range(1, 70)]) # Karl V. Keller, Jr., Aug 07 2020

A108591 Self-inverse integer permutation induced by Beatty sequences for Pi and Pi/(Pi-1).

Original entry on oeis.org

3, 6, 1, 9, 12, 2, 15, 18, 4, 21, 25, 5, 28, 31, 7, 34, 37, 8, 40, 43, 10, 47, 50, 53, 11, 56, 59, 13, 62, 65, 14, 69, 72, 16, 75, 78, 17, 81, 84, 19, 87, 91, 20, 94, 97, 100, 22, 103, 106, 23, 109, 113, 24, 116, 119, 26, 122, 125, 27, 128, 131, 29, 135, 138, 30, 141, 144

Offset: 1

Reinhard Zumkeller, Jun 11 2005

Eric Weisstein's World of Mathematics, Beatty Sequence
Index entries for sequences that are permutations of the natural numbers
Index entries for sequences related to Beatty sequences

Cf. A108590, A108592, A108599.

a(A022844(n))=A054386(n) and a(A054386(n))=A022844(n).

a(53)/a(54) joined by Georg Fischer, May 24 2022

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A022843 Beatty sequence for e: a(n) = floor(n*e).

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A054385 Beatty sequence for e/(e-1); complement of A022843.

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Programs

Haskell

Maple

Mathematica

Python

A108591 Self-inverse integer permutation induced by Beatty sequences for Pi and Pi/(Pi-1).

Views

Author

Keywords

Links

Crossrefs

Formula

Extensions