%I A133501
%S A133501 0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,5,2,3,3,1,1,1,3,2,
%T A133501 5,5,5,4,9,1,1,2,5,3,3,4,6,3,5,1,1,3,2,3,5,3,3,2,4,1,1,6,3,4,4,3,3,8,2,
%U A133501 1,1,6,6,2,2,3,5,3,2,1,1,5,3,4,4,5,4,3,7,1,1,2,5,4,2,3,3,2,4,1,1,1,1,1
%N A133501 Number of steps for "powertrain" operation to converge when started at 
               n.
%C A133501 See A133500 for definition.
%C A133501 It is conjectured that every number converges to a single number.
%H A133501 N. J. A. Sloane, <a href="b133501.txt">Table of n, a(n) for n = 0..10000</
               a>
%H A133501 N. J. A. Sloane, <a href="a133501.txt">Full trajectories of numbers from 
               1 to 10000</a>
%e A133501 39 -> 19683 -> 1594323 -> 38443359375 -> 59440669655040 -> 0, so a(39) 
               = 5.
%p A133501 powertrain:=proc(n) local a,i,n1,n2,t1,t2; n1:=abs(n); n2:=sign(n); t1:=convert(n1, 
               base, 10); t2:=nops(t1); a:=1; for i from 0 to floor(t2/2)-1 do a 
               := a*t1[t2-2*i]^t1[t2-2*i-1]; od: if t2 mod 2 = 1 then a:=a*t1[1]; 
               fi; RETURN(n2*a); end;
%p A133501 # Compute trajectory of n under repeated application of the powertrain 
               map of A133500. This will return -1 if the trajectory does not converge 
               to a single number in 100 steps (so it could fail if the trajectory 
               enters a nontrivial loop or takes longer than 100 steps to converge).
%p A133501 PTtrajectory := proc(n) local p,M,t1,t2,i; M:=100; p:=[n]; t1:=n; for 
               i from 1 to M do t2:=powertrain(t1); if t2 = t1 then RETURN(n,i-1,
               p); fi; t1:=t2; p:=[op(p),t2]; od; RETURN(n,-1,p); end;
%Y A133501 See A133508, A133503 for records. See A135381 for high-water marks.
%Y A133501 Sequence in context: A159580 A021448 A108053 this_sequence A124316 A061034 
               A111861
%Y A133501 Adjacent sequences: A133498 A133499 A133500 this_sequence A133502 A133503 
               A133504
%K A133501 nonn,base
%O A133501 0,25
%A A133501 J. H. Conway and N. J. A. Sloane (njas(AT)research.att.com), Dec 03 2007