|
Search: id:A056154
|
|
|
| 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). |
|
+0
4
|
|
| 5, 27, 40, 92, 138, 929, 1086, 352664, 4976816, 9914261, 23434996, 30490425
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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.
|
|
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: A039283 A045162 A056735 this_sequence A058490 A136917 A048712
Adjacent sequences: A056151 A056152 A056153 this_sequence A056155 A056156 A056157
|
|
KEYWORD
|
hard,more,nonn
|
|
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
|
|
|
Search completed in 0.002 seconds
|
