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 A056154 Numbers n such that the number of times each digit occurs in 2^n, represented in base 3, is the same as 2^(n+1), also represented in base 3. Or in other words, when represented in base 3, the digits in 2^n can be rearranged to form 2^(n+1). 4
 5, 27, 40, 92, 138, 929, 1086, 352664, 4976816, 9914261, 23434996, 30490425, 49094174 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For powers of 2 less than 2^1000, representations in base 3 are the only nontrivial examples where these kinds of pairs can be found. In other bases, for any integer n > 1, 2^(n+2) has the same frequency of digits as 2^(2n), represented in base (2^n)+1 (e.g., 2^3 and 2^4 in base 5, 2^4 and 2^6 in base 9, 2^5 and 2^8 in base 17, etc.). For any n > 0, it can be shown that the distribution of these terms is approximately k*log(n), with k a small constant. This distribution can be derived from empirical evidence detailed in sequences A056734, A056735 and A056736. LINKS J. Frech, Extending A056154, 2019. EXAMPLE First term: 2^5 = 1012 and 2^6 = 2101 -> number of occurrences of 0, 1 and 2 are {1 2 1}; second term: 2^27 = 100100112222002222 and 2^28 = 200201002221012221 -> {6 4 8}. CROSSREFS Cf. A056734, A056735, A056736. Sequence in context: A045162 A056735 A298441 * A156215 A058490 A299578 Adjacent sequences:  A056151 A056152 A056153 * A056155 A056156 A056157 KEYWORD hard,more,nonn,base AUTHOR Russell Harper (rharper(AT)intouchsurvey.com), Jul 30 2000 EXTENSIONS More terms from Bruce G. Stewart (bstewart(AT)bix.com), Aug 28 2000 and Sep 15 2000 a(13) from Jonathan Frech, Oct 31 2019 STATUS approved

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Last modified May 24 18:33 EDT 2020. Contains 334580 sequences. (Running on oeis4.)