OFFSET
1,1
COMMENTS
Using empirical data for 1 <= k <= 10000, it has been found that the distribution of these terms correlates well (R^2 = 0.9798) with g(k) = b*sqrt(k) where b ~ 0.70. In addition, g'(k) approximates the probability that any particular k has this property. A056154 is a subsequence.
EXAMPLE
a(1)=5: 2^5 = 1012_3, 2^6 = 2101_2, both with two 1's and both of length 4.
a(2)=27: 2^27 = 100100112222002222_3, 2^28 = 200201002221012221_3, both with four 1's and both of length 18.
MATHEMATICA
Select[Range[4100], Length[IntegerDigits[2^#, 3]]==Length[ IntegerDigits[ 2^(#+1), 3]] && DigitCount[2^#, 3, 1]==DigitCount[2^(#+1), 3, 1]&] (* Harvey P. Dale, Jul 09 2021 *)
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
Russell Harper (rharper(AT)intouchsurvey.com), Aug 13 2000
STATUS
approved