A121384 -id:A121384 - 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

A022852 Integer nearest n * e, where e is the natural log base.

Original entry on oeis.org

0, 3, 5, 8, 11, 14, 16, 19, 22, 24, 27, 30, 33, 35, 38, 41, 43, 46, 49, 52, 54, 57, 60, 63, 65, 68, 71, 73, 76, 79, 82, 84, 87, 90, 92, 95, 98, 101, 103, 106, 109, 111, 114, 117, 120, 122, 125, 128, 130, 133, 136, 139, 141, 144, 147, 150, 152, 155, 158, 160

Offset: 0

Clark Kimberling

nonn

A022843(n) <= a(n) <= A121384(n). - Reinhard Zumkeller, Mar 17 2015

			2 * e = 5.436563656918..., so a(2) = 5.
3 * e = 8.1548454853771357..., so a(3) = 8.
4 * e = 10.87312731383618..., so a(4) = 11.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Cf. A001113, A022843, A121384.

a022852 = round . (* exp 1) . fromIntegral
-- Reinhard Zumkeller, Mar 17 2015

[Round(n*Exp(1)): n in [0..60]]; // G. C. Greubel, Sep 29 2018

Round[E * Range[0, 60]] (* Harvey P. Dale, Jan 08 2014 *)

a(n)=n*exp(1)\1 \\ Charles R Greathouse IV, Jan 08 2014

(0L to 59L).map(n => Math.round(n * Math.E)) // Alonso del Arte, Dec 14 2018

Zero prepended by Harvey P. Dale, Jan 08 2014

A325735 First term of n-th difference sequence of (floor(-k*e)), k >= 0.

Original entry on oeis.org

-3, 0, 0, 1, -4, 10, -20, 36, -64, 120, -239, 484, -946, 1716, -2794, 3872, -3872, 1, 14160, -52478, 143716, -345400, 767976, -1613128, 3226257, -6148960, 11119030, -18874260, 29414650, -39955040, 39955040, 1, -151615948, 575723786, -1611404740, 3936821260

Offset: 1

Clark Kimberling, May 20 2019

Inverse binomial transform of A121384 (values negated). - R. J. Mathar, Jun 17 2019

Clark Kimberling, Table of n, a(n) for n = 1..200

Cf. A325664.

Table[First[Differences[Table[Floor[-E*n], {n, 0, 50}], n]], {n, 1, 50}]

A319795 a(n) = n^(n+1)/(n-1)^n for n>1, rounded to nearest integer.

Original entry on oeis.org

8, 10, 13, 15, 18, 21, 23, 26, 29, 31, 34, 37, 40, 42, 45, 48, 50, 53, 56, 59, 61, 64, 67, 69, 72, 75, 78, 80, 83, 86, 88, 91, 94, 97, 99, 102, 105, 107, 110, 113, 116, 118, 121, 124, 126, 129, 132, 135, 137, 140, 143, 145, 148, 151, 154, 156, 159, 162, 164

Offset: 2

Jim Singh, Sep 28 2018

Cf. A084363, A022852, A121384.

seq(round(n^(n+1)/(n-1)^n),n=1..100); # Muniru A Asiru, Sep 28 2018

for(n=2,30,print1(round(n^(n+1)/(n-1)^n),","))

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Magma

Maple

Mathematica

PARI

Python

Formula

A022852 Integer nearest n * e, where e is the natural log base.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

Magma

Mathematica

PARI

Scala

Extensions

A325735 First term of n-th difference sequence of (floor(-k*e)), k >= 0.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A319795 a(n) = n^(n+1)/(n-1)^n for n>1, rounded to nearest integer.

Views

Author

Keywords

Crossrefs

Programs

Maple

PARI