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.
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
KEYWORD
easy,nonn,base
AUTHOR
Russell Harper (rharper(AT)intouchsurvey.com), Aug 13 2000
STATUS
approved