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Search: id:A059884
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| A059884 |
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Prime factorization of n encoded by recursively interleaving bits of successive prime exponents. |
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+0
8
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| 0, 1, 2, 4, 8, 3, 128, 5, 32, 9, 32768, 6, 2147483648, 129, 10, 16, 9223372036854775808, 33, 170141183460469231731687303715884105728, 12, 130, 32769
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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For n=2^e0*3^e1*5^e2... the alternate (i.e. 2^0,2,4...) bit positions of a(n) give e0, the alternate *remaining* bit positions (i.e. 2^1,5,9...) give e1, the *remaining* alternates (i.e. 2^3,11,19...) give e2, and so on. (Any finite vector of nonnegative integers can be uniquely encoded this way.) Every nonnegative integer appears exactly once in this sequence-despite its outlandish behavior: the next term, a(29) is 2^511 (which has 153 digits), followed by a(30)=11...
Inverse of sequence A059900 considered as a permutation of the nonnegative integers. - Howard A. Landman (howard(AT)polyamory.org), Sep 25 2001
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LINKS
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Index entries for sequences that are permutations of the natural numbers
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EXAMPLE
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a(360)=a(2^3 * 3^2 * 5^1)=45 thus: ...0 0 0 0 0 0 1 1 -> 3 from 2^3 ...0 0 1 0 -> 2 from 3^2 ...0 1 -> 1 from 5^1 ...00000101101 == 45.
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CROSSREFS
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Cf. A075173, A075300, A075302.
Sequence in context: A109588 A052331 A119436 this_sequence A021805 A031401 A078479
Adjacent sequences: A059881 A059882 A059883 this_sequence A059885 A059886 A059887
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KEYWORD
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easy,nonn
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AUTHOR
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Marc LeBrun (mlb(AT)well.com), Feb 06 2001
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