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Search: id:A056736
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| A056736 |
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Numbers n such that 2^n in base 3 has same number of 2's as 2^(n+1) in base 3 and 2^n and 2^(n+1) have the same number of digits in base 3. |
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2
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| 5, 16, 27, 40, 65, 92, 124, 138, 143, 265, 368, 457, 476, 501, 634, 707, 839, 842, 848, 929, 1013, 1086, 1289, 1303, 1587, 1685, 1812, 1926, 1994, 2213, 2308, 2522, 2565, 2950, 3286, 3674, 3774, 3942, 4034, 4318, 4381, 4438, 4719, 4728, 4909, 4971
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OFFSET
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1,1
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COMMENT
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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.
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EXAMPLE
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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.
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CROSSREFS
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A056154.
Sequence in context: A018197 A061874 A017449 this_sequence A063236 A063228 A063135
Adjacent sequences: A056733 A056734 A056735 this_sequence A056737 A056738 A056739
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KEYWORD
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easy,nonn,base
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AUTHOR
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Russell Harper (rharper(AT)intouchsurvey.com), Aug 13 2000
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