

A115566


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


1



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
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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 * A190507 A087298 A237707
Adjacent sequences: A115563 A115564 A115565 * A115567 A115568 A115569


KEYWORD

nonn,base


AUTHOR

Stefan Steinerberger, Mar 11 2006


STATUS

approved



