%I A063574
%S A063574 0,2,1,2,0,1,2,4,0,4,1,3,0,1,3,4,0,2,1,2,0,1,2,3,0,3,1,7,0,1,4,6,0,2,1,
%T A063574 2,0,1,2,5,0,6,1,3,0,1,3,5,0,2,1,2,0,1,2,3,0,3,1,4,0,1,5,6,0,2,1,2,0,1,
%U A063574 2,4,0,4,1,3,0,1,3,4,0,2,1,2,0,1,2,3,0,3,1,5,0,1,4,5,0,2,1,2,0,1,2,7,0
%N A063574 Number of steps to reach an integer == 1 (mod 4) when iterating the map 
               n -> 3n/2 if n even or (3n+1)/2 if n odd.
%D A063574 L. Flatto, Z-numbers and beta-transformations, in Symbolic dynamics and 
               its applications (New Haven, CT, 1991), 181-201, Contemp. Math., 
               135, Amer. Math. Soc., Providence, RI, 1992.
%D A063574 K. Mahler, An unsolved problem on the powers of 3/2, J. Austral. Math. 
               Soc. 8 1968 313-321.
%F A063574 For odd n: a(n)=A007814(n+1), for even n: A007814(n) steps until an odd 
               number is reached, which leads directly to the formula: with b(n)=A007814(n) 
               (binary carry sequence) a(n)=b(n)+b((3^b(n)*n/2^b(n)+1)/2) - Lambert 
               Herrgesell (zero815(AT)googlemail.com) and Lambert Klasen (lambert.klasen(AT)gmx.net), 
               Apr 24 2006. Hence in particular, a(n) is well-defined.
%e A063574 8 -> 12 -> 18 -> 27 -> 41 takes 4 steps so a(8) = 4.
%o A063574 PARI {stop=1000; for(n=1,105,c=0; k=n; while((k%4)!=1&&c<stop,k=if(k%2==0,
               3*k/2,(3*k+1)/2); c++); print1(if(c<stop,c,-1),","))}
%o A063574 (PARI) b(n)=valuation(n,2); a(n)=b(n)+b((3^b(n)*n/2^b(n)+1)/2) - Lambert 
               Herrgesell (zero815(AT)googlemail.com) and Lambert Klasen (lambert.klasen(AT)gmx.net), 
               Apr 24 2006
%Y A063574 Cf. A007494.
%Y A063574 Sequence in context: A114004 A049986 A137289 this_sequence A144515 A028933 
               A143352
%Y A063574 Adjacent sequences: A063571 A063572 A063573 this_sequence A063575 A063576 
               A063577
%K A063574 easy,nice,nonn
%O A063574 1,2
%A A063574 N. J. A. Sloane (njas(AT)research.att.com), Sep 23 2002
%E A063574 Extended by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Sep 23 
               2002