A066344 -id:A066344 - cp's OEIS frontend

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

Vladeta Jovovic, Dec 15 2001

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

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

Cf. A066344, A067497, A129344.

Cf. A020862 (log_2(10)).

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

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

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

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

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

A226721 Position of 2^n in the joint ranking of all the numbers 2^j for j>=0 and 5^k for k>=1; complement of A123384.

Original entry on oeis.org

2, 3, 5, 6, 8, 9, 11, 12, 13, 15, 16, 18, 19, 21, 22, 23, 25, 26, 28, 29, 31, 32, 33, 35, 36, 38, 39, 41, 42, 43, 45, 46, 48, 49, 51, 52, 53, 55, 56, 58, 59, 61, 62, 63, 65, 66, 68, 69, 71, 72, 73, 75, 76, 78, 79, 81, 82, 83, 85, 86, 88, 89, 91, 92, 93, 95

Offset: 1

Clark Kimberling, Jun 16 2013

			The joint ranking of the powers of 2 and of 5 begins like this: 1, 2, 4, 5, 8, 16, 25, 32, 64, 125, 128, 256, 512.  The numbers 2^n for n >= 1 are in positions 2, 3, 5, 6, 8, 9, 11, 12, 13.

Clark Kimberling, Table of n, a(n) for n = 1..2000

Cf. A123384, A226720.

b = 2; c=5; Floor[1 + Range[0, 100]*(1 + Log[b, c])]  (* A123384 *)
Floor[1 + Range[1, 100]*(1 + Log[c, b])]  (* A226721 *)

a(n) = 1 + A066344(n).

a(n) = 1 + floor(n*(1 + log_5(2))).

A175852 a(n) = the highest power of 5 with n decimal digits.

Original entry on oeis.org

5, 25, 625, 3125, 78125, 390625, 9765625, 48828125, 244140625, 6103515625, 30517578125, 762939453125, 3814697265625, 95367431640625, 476837158203125, 2384185791015625, 59604644775390625, 298023223876953125

Offset: 1

Zak Seidov, Sep 29 2010

a(n) = 5^d(n), with
d(n) = {1, 2, 4, 5, 7, 8, 10, 11, 12, 14, 15, 17, 18, 20, 21, 22, 24, 25, 27, 28}.
If we redefine the sequence as a(n) = the highest power of 5 less than 10^n, then keyword "base" may be omitted.
d(n) = A066344(n). - Zak Seidov, Oct 01 2010

Mathematica
```
d[n_]=Floor@Log[5, 10^n]; a[n_]=5^d[n]
```

cp's OEIS Frontend

A066343 Beatty sequence for log_2(10).

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A226721 Position of 2^n in the joint ranking of all the numbers 2^j for j>=0 and 5^k for k>=1; complement of A123384.

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A175852 a(n) = the highest power of 5 with n decimal digits.

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