A059884 Prime factorization of n encoded by recursively interleaving bits of successive prime exponents.

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

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 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, 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: A225124 A344537 A349104 * A191561 A021805 A031401

Adjacent sequences: A059881 A059882 A059883 * A059885 A059886 A059887

Keyword

easy,nonn

Author

Marc LeBrun, Feb 06 2001

Status

approved