%I
%S 0,1,2,4,8,3,128,5,32,9,32768,6,2147483648,129,10,16,
%T 9223372036854775808,33,170141183460469231731687303715884105728,12,
%U 130,32769
%N Prime factorization of n encoded by recursively interleaving bits of successive prime exponents.
%C 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...
%C Inverse of sequence A059900 considered as a permutation of the nonnegative integers.  _Howard A. Landman_, Sep 25 2001
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e 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.
%Y Cf. A075173, A075300, A075302.
%K easy,nonn
%O 1,3
%A _Marc LeBrun_, Feb 06 2001
