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Search: id:A056734
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| A056734 |
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Numbers n such that 2^n in base 3 has same number of 0'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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+0
2
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| 2, 5, 8, 10, 18, 21, 27, 29, 35, 40, 62, 67, 83, 92, 138, 146, 165, 184, 298, 346, 428, 487, 666, 750, 785, 929, 937, 1064, 1086, 1156, 1162, 1240, 1614, 1706, 1739, 1788, 2327, 2389, 2533, 2649, 2937, 3240, 3403, 3489, 3549, 3619, 3693, 3817, 3866, 4175
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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 = 0.9513) to f(n) = a*n^(1/2) with 'a' a constant approximately 0.73. In addition, f'(n) approximates the probability that any particular n has this property. Any terms in A056154 must also satisfy this sequence.
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EXAMPLE
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First term: 2^2 = 11, 2^3 = 22, both with 0 zeros and both of length 2. Second term: 2^5 = 1012, 2^6 = 2101, both with 1 zero and both of length 4.
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CROSSREFS
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A056154.
Sequence in context: A030713 A157481 A100809 this_sequence A019995 A031141 A143263
Adjacent sequences: A056731 A056732 A056733 this_sequence A056735 A056736 A056737
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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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