A059545 -id:A059545 - cp's OEIS frontend

A059546 Beatty sequence for log(10)/(log(10)-1).

1, 3, 5, 7, 8, 10, 12, 14, 15, 17, 19, 21, 22, 24, 26, 28, 30, 31, 33, 35, 37, 38, 40, 42, 44, 45, 47, 49, 51, 53, 54, 56, 58, 60, 61, 63, 65, 67, 68, 70, 72, 74, 76, 77, 79, 81, 83, 84, 86, 88, 90, 91, 93, 95, 97, 98, 100, 102, 104, 106, 107, 109, 111, 113, 114, 116

Offset: 1

Mitch Harris, Jan 22 2001

Harry J. Smith, Table of n, a(n) for n = 1..2000
Aviezri S. Fraenkel, Jonathan Levitt, Michael Shimshoni, Characterization of the set of values f(n)=[n alpha], n=1,2,..., Discrete Math. 2 (1972), no.4, 335-345.
Eric Weisstein's World of Mathematics, Beatty Sequence.
Index entries for sequences related to Beatty sequences

Beatty complement is A059545.

Cf. A002392.

Floor[Range[100]*(1 + 1/(Log[10] - 1))] (* Paolo Xausa, Jul 05 2024 *)

{ default(realprecision, 100); b=log(10)/(log(10) - 1); for (n = 1, 2000, write("b059546.txt", n, " ", floor(n*b)); ) } \\ Harry J. Smith, Jun 28 2009

a(n) = floor(n*log(10)/(log(10) - 1)). - Michel Marcus, Jan 04 2015

A334168 Numbers m whose leading digit and the other decimal digits appear respectively before and directly after the decimal point of its m-th root.

Original entry on oeis.org

1, 12, 104, 1006, 10009, 100011, 1000013, 10000016, 100000018, 1000000020, 10000000023, 100000000025, 1000000000027, 10000000000029, 100000000000032, 1000000000000034, 10000000000000036, 100000000000000039, 1000000000000000041, 10000000000000000043

Offset: 1

Alaa A. Nasr, Apr 17 2020

These numbers m are equal to the integer part of their m-th root multiplied by 10 to the power of the number of digits of m-1.

The last nonzero digits of the terms are conjectured to be the Beatty sequence for log(10), A059545.

			12^(1/12) = 1.23007..., 104^(1/104) = 1.0457..., 100011^(1/100011) = 1.00011512...

Cf. A059545.

isok(m) = floor(10^(#Str(m)-1)*sqrtn(m, m)) == m; \\ Michel Marcus, Apr 17 2020

# for the first 6 terms
import math
for n in range(1, 1000000):
    if math.floor((n**(1/n))*10**(len(str(n))-1)) == n:
        print(n)

a(n+1) = floor((10^(n/10^n))*10^n) (conjectured).

a(n) = 10^(n-1) + floor((n-1)*log(10)) (conjectured). - David A. Corneth, Apr 19 2020

More terms from David A. Corneth, Apr 19 2020

cp's OEIS Frontend

A059546 Beatty sequence for log(10)/(log(10)-1).

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A334168 Numbers m whose leading digit and the other decimal digits appear respectively before and directly after the decimal point of its m-th root.

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