%I A133500
%S A133500 0,1,2,3,4,5,6,7,8,9,1,1,1,1,1,1,1,1,1,1,1,2,4,8,16,32,64,128,256,512,
               1,
%T A133500 3,9,27,81,243,729,2187,6561,19683,1,4,16,64,256,1024,4096,16384,65536,
%U A133500 262144,1,5,25,125,625,3125,15625,78125,390625,1953125,1,6,36,216,1296
%N A133500 Powertrain(n): if abcd... is the decimal expression of a number n, then 
               the powertrain of n is the number n' = a^b*c^d* ..., which ends in 
               an exponent or a base according as the number of digits is even or 
               odd. a(0) = 0 by convention.
%C A133500 We take 0^0 = 1.
%C A133500 The fixed points are in A135385.
%H A133500 N. J. A. Sloane, <a href="b133500.txt">Table of n, a(n) for n = 0..10000</
               a>
%p A133500 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; - N. J. A. Sloane (njas(AT)research.att.com), 
               Dec 03 2007
%Y A133500 Cf. A133501-A133502, A135385. For records see A133504, A133505.
%Y A133500 Cf. A133048 (powerback), A031346 and A003001 (persistence).
%Y A133500 Sequence in context: A055017 A040997 A075877 this_sequence A052423 A126616 
               A121042
%Y A133500 Adjacent sequences: A133497 A133498 A133499 this_sequence A133501 A133502 
               A133503
%K A133500 nonn,base
%O A133500 0,3
%A A133500 John Conway, Dec 03 2007