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

1,2

Comments

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

Links

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

Formula

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

Example

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.

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)] &]

Prog

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

Crossrefs

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

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

Sequence in context: A223024 A275340 A082206 * A364840 A190507 A087298

Adjacent sequences: A115563 A115564 A115565 * A115567 A115568 A115569

Keyword

nonn,base

Author

Stefan Steinerberger, Mar 11 2006

Status

approved