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).

5, 27, 40, 92, 138, 929, 1086, 352664, 4976816, 9914261, 23434996, 30490425, 49094174

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..13.

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