A115566 Numbers k such that 2^k, 2^(k+1) and 2^(k+2) have the same number of digits.

1, 4, 7, 10, 11, 14, 17, 20, 21, 24, 27, 30, 31, 34, 37, 40, 41, 44, 47, 50, 51, 54, 57, 60, 61, 64, 67, 70, 71, 74, 77, 80, 81, 84, 87, 90, 91, 94, 97, 100, 103, 104, 107, 110, 113, 114, 117, 120, 123, 124, 127, 130, 133, 134, 137, 140, 143, 144, 147, 150, 153, 154

Offset: 1

Author

Stefan Steinerberger, Mar 11 2006

Keywords

• nonn
• base

Comments

The density of this sequence is 1 - 2*log_10(2) = 0.3979400086720376...

Examples

			2^4 = 16, 2^5 = 32, 2^6 = 64: all these numbers have two digits.
2^10 = 1024, 2^11 = 2048, 2^12 = 4096: all these numbers have three digits.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001682 (same definition with 3 instead of 2).

Cf. A034887 (number of digits in 2^n).

Programs

Magma

[k:k in [1..160]|#Intseq(2^k) eq #Intseq(2^(k+2))]; // Marius A. Burtea, May 20 2019

Maple

select(n -> ilog10(2^n)=ilog10(2^(n+2)), [$1..1000]); # Robert Israel, May 19 2019

Mathematica

Select[Range[220], Floor[Log[10, 2]*# ] == Floor[Log[10, 2]*(# + 2)] &]

Formula

floor(log_10(2)*k) = floor(log_10(2)*(k+1)) = floor(log_10(2)*(k+2)).