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

Author

Clark Kimberling

Keywords

• nonn

Comments

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

Links

• 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

Crossrefs

Cf. A054385, A108599.

Cf. A001113 (e), A022852, A121384.

Programs

Haskell

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

Magma

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

Maple

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

Mathematica

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

PARI

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

Python

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

Formula

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