A066343 Beatty sequence for log_2(10).

3, 6, 9, 13, 16, 19, 23, 26, 29, 33, 36, 39, 43, 46, 49, 53, 56, 59, 63, 66, 69, 73, 76, 79, 83, 86, 89, 93, 96, 99, 102, 106, 109, 112, 116, 119, 122, 126, 129, 132, 136, 139, 142, 146, 149, 152, 156, 159, 162, 166, 169, 172, 176, 179, 182, 186, 189, 192, 195, 199

Offset: 1

Author

Vladeta Jovovic, Dec 15 2001

Keywords

• easy
• nonn

Comments

Number of positive integers <= 10^n that are divisible by no prime exceeding 2.

Maximum number of prime divisors of positive integers <= 10^n counted with multiplicity. - Martin Renner, Apr 04 2014

You wish to represent the rational number n/d in decimal notation, where n is an integer, d is a nonzero integer, and precision(d) represents the number of decimal digits in d. The decimal notation representation of n/d will either terminate or repeat with a repetend. If the decimal notation representation terminates then this sequence defines the maximum number of decimal digits to the right of the decimal point (after truncating trailing zeros) for a given precision of d ... floor(precision(d) * log_2(10)). - Michael T Howard, Jul 17 2017

Beatty complement of A066344. - Jianing Song, Jan 27 2019

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Beatty Sequence

Crossrefs

Cf. A066344, A067497, A129344.

Cf. A020862 (log_2(10)).

Programs

Maple

seq(floor(log[2](10)*n),n=1..60); # Martin Renner, Apr 04 2014

Mathematica

Table[ Floor[ n*Log[2, 10]], {n, 60}] (* Robert G. Wilson v, May 27 2005 *)

PARI

{ l=log(10)/log(2); for (n=1, 1000, a=floor(n*l); write("b066343.txt", n, " ", a) ) } \\ Harry J. Smith, Feb 11 2010

Python

def A066343(n): return (5**n).bit_length()+n-1 # Chai Wah Wu, Sep 08 2024

Formula

a(n) = floor(n*log_2(10)).