

A059884


Prime factorization of n encoded by recursively interleaving bits of successive prime exponents.


7



0, 1, 2, 4, 8, 3, 128, 5, 32, 9, 32768, 6, 2147483648, 129, 10, 16, 9223372036854775808, 33, 170141183460469231731687303715884105728, 12, 130, 32769
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OFFSET

1,3


COMMENTS

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 sequencedespite 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, Sep 25 2001


LINKS

Table of n, a(n) for n=1..22.
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

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.


CROSSREFS

Cf. A075173, A075300, A075302.
Sequence in context: A223699 A231610 A225124 * A191561 A021805 A031401
Adjacent sequences: A059881 A059882 A059883 * A059885 A059886 A059887


KEYWORD

easy,nonn


AUTHOR

Marc LeBrun, Feb 06 2001


STATUS

approved



