A001682 -id:A001682 - cp's OEIS frontend

A151910 First differences of A001682.

21, 21, 23, 21, 23, 21, 21, 23, 21, 23, 21, 23, 21, 21, 23, 21, 23, 21, 23, 21, 21, 23, 21, 23, 21, 23, 21, 21, 23, 21, 23, 21, 23, 21, 21, 23, 21, 23, 21, 23, 21, 21, 23, 21, 23, 21, 23, 21, 21, 23, 21, 23, 21, 23, 21, 21, 23

Offset: 1

Harvey P. Dale, Aug 08 2009

nonn

a(n) = A001682(n+1) - A001682(n).

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

a151910 n = a151910_list !! (n-1)
a151910_list = zipWith (-) (tail a001682_list) a001682_list
-- Reinhard Zumkeller, Oct 10 2011

Offset corrected and initial term added by Reinhard Zumkeller, Oct 10 2011

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

Original entry on oeis.org

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

Stefan Steinerberger, Mar 11 2006

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

			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.

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

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

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

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

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

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

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

cp's OEIS Frontend

A151910 First differences of A001682.

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

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