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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). 3
5, 27, 40, 92, 138, 929, 1086, 352664, 4976816, 9914261, 23434996, 30490425 (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

Table of n, a(n) for n=1..12.

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

STATUS

approved

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Last modified March 23 16:52 EDT 2019. Contains 321432 sequences. (Running on oeis4.)