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Search: id:A115566
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| A115566 |
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Numbers n such that 2^n, 2^(n+1) and 2^(n+2) have the same number of digits. |
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+0
1
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| 1, 4, 7, 10, 11, 14, 17, 20, 21, 24, 27, 30, 31, 34, 37, 40, 41, 44, 47, 50, 51, 54, 57, 60, 61, 64, 67, 70, 71, 74, 77, 80, 81, 84, 87, 90, 91, 94, 97, 100, 103, 104, 107, 110, 113, 114, 117, 120, 123, 124, 127, 130, 133, 134, 137, 140, 143, 144, 147, 150, 153, 154
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The density of this sequence is 1-2*Log[2], which is approximately 0.3979400087 (Log is base 10).
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FORMULA
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Floor[Log[2]*n] = Floor[Log[2]*(n+1)] = Floor[Log[2]*(n+2)] (Log is to base 10)
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EXAMPLE
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2^4 = 16, 2^5 = 32, 2^6 = 64: all these numbers have two digits.
2^10 = 1024, 2^11 = 2048, 2^12 = 4096: all these numbers have three digits.
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MATHEMATICA
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Select[Range[220], Floor[Log[10, 2]*# ] == Floor[Log[10, 2]*(# + 2)] &]
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CROSSREFS
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Cf. A001682 [same definition with 3 instead of 2].
Cf. A082206.
Sequence in context: A123869 A072125 A082206 this_sequence A087298 A127958 A000414
Adjacent sequences: A115563 A115564 A115565 this_sequence A115567 A115568 A115569
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KEYWORD
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nonn,base
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AUTHOR
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Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 11 2006
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