%I A080825
%S A080825 1,2,1,2,1,4,2,1,3,2,1,6,3,2,1,4,2,1,8,4,2,1,5,4,2,1,10,5,4,2,1,6,3,2,
%T A080825 1,12,6,3,2,1,7,6,3,2,1,14,7,6,3,2,1,8,4,2,1,16,8,4,2,1,9,8,4,2,1,18,9,
%U A080825 8,4,2,1,10,5,4,2,1,20,10,5,4,2,1,11,10,5,4,2,1,22,11,10,5,4,2,1,12,6,
               3
%N A080825 Triangle read by rows in which n-th row gives trajectory of n (omitting 
               n itself) under the map k -> k-1 if k odd, k -> k/2 if k even.
%C A080825 If you write down 0 when divide by 2, 1 when subtract 1, the trajectory 
               gives the binary expansion of n.
%e A080825 Triangle begins:
%e A080825 1;
%e A080825 2,1;
%e A080825 2,1;
%e A080825 4,2,1;
%e A080825 3,2,1;
%e A080825 6,3,2,1;
%e A080825 ...
%e A080825 7 -> 6 -> 3 -> 2 -> 1, so the 7-th row is 6,3,2,1.
%o A080825 (PARI) xnm1(n,p) = { print1(1" "); for(x=1,n, p1 = x; while(p1>1, if(p1%2==0,
               p1/=2,p1 = p1*p-1;); print1(p1" ") ) ) }
%Y A080825 A082404 is a better version.
%Y A080825 Sequence in context: A061797 A068341 A100380 this_sequence A034693 A072342 
               A066389
%Y A080825 Adjacent sequences: A080822 A080823 A080824 this_sequence A080826 A080827 
               A080828
%K A080825 easy,nonn,tabf
%O A080825 2,2
%A A080825 Cino Hilliard (hillcino368(AT)gmail.com), Mar 27 2003
%E A080825 Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 06 2008 at 
               the suggestion of R. J. Mathar