A056736 Numbers n such that 2^n in base 3 has same number of 2's as 2^(n+1) in base 3 and 2^n and 2^(n+1) have the same number of digits in base 3.

5, 16, 27, 40, 65, 92, 124, 138, 143, 265, 368, 457, 476, 501, 634, 707, 839, 842, 848, 929, 1013, 1086, 1289, 1303, 1587, 1685, 1812, 1926, 1994, 2213, 2308, 2522, 2565, 2950, 3286, 3674, 3774, 3942, 4034, 4318, 4381, 4438, 4719, 4728, 4909, 4971

Offset

1,1

Comments

Using empirical data for 1 <= n <= 10000, it has been found that the distribution of these terms correlates well (R^2 = 0.9936) to h(n) = c*n^(1/2) with 'c' a constant approximately 0.64. In addition, h'(n) approximates the probability that any particular n has this property. Any terms in sequence A056154 must also satisfy this sequence.

Links

Table of n, a(n) for n=1..46.

Example

First term: 2^5 = 1012, 2^6 = 2101, both with 1 two and both of length 4. Second term: 2^16 = 10022220021, 2^17 = 20122210112, both with 5 twos and both of length 11.

Mathematica

sn2Q[n_]:=Module[{a=2^n, b=2^(n+1)}, DigitCount[a, 3, 2]==DigitCount[b, 3, 2] && IntegerLength[a, 3]==IntegerLength[b, 3]]; Select[Range[5000], sn2Q] (* Harvey P. Dale, Aug 27 2012 *)

Crossrefs

A056154.

Sequence in context: A061874 A341006 A017449 * A063236 A063228 A063135

Adjacent sequences: A056733 A056734 A056735 * A056737 A056738 A056739

Keyword

easy,nonn,base

Author

Russell Harper (rharper(AT)intouchsurvey.com), Aug 13 2000

Status

approved