cp's OEIS Frontend

A133500 The powertrain or power train map: Powertrain(n): if abcd... is the decimal expansion 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.

%I A133500 #41 Nov 29 2021 14:40:59
%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,
%T A133500 1,3,9,27,81,243,729,2187,6561,19683,1,4,16,64,256,1024,4096,16384,
%U A133500 65536,262144,1,5,25,125,625,3125,15625,78125,390625,1953125,1,6,36,216,1296
%N A133500 The powertrain or power train map: Powertrain(n): if abcd... is the decimal expansion 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.
%C A133500 For 1-digit or 2-digit numbers this is the same as A075877. - R. J. Mathar, Mar 28 2012
%C A133500 a(A221221(n)) = A133048(A221221(n)) = A222493(n). - _Reinhard Zumkeller_, May 27 2013
%H A133500 N. J. A. Sloane, <a href="/A133500/b133500.txt">Table of n, a(n) for n = 0..10000</a>
%H A133500 N. J. A. Sloane, <a href="/A195264/a195264.pdf">Confessions of a Sequence Addict (AofA2017)</a>, slides of invited talk given at AofA 2017, Jun 19 2017, Princeton. Mentions this sequence.
%H A133500 N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, <a href="https://vimeo.com/237029685">Part I</a>, <a href="https://vimeo.com/237030304">Part 2</a>, <a href="https://oeis.org/A290447/a290447_slides.pdf">Slides.</a> (Mentions this sequence)
%e A133500 20 -> 2^0 = 1,
%e A133500 21 -> 2^1 = 2,
%e A133500 24 -> 2^4 = 16,
%e A133500 39 -> 3^9 = 19683,
%e A133500 623 -> 6^2*3 = 108,
%e A133500 etc.
%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_, Dec 03 2007
%t A133500 ptm[n_]:=Module[{idn=IntegerDigits[n]},If[EvenQ[Length[idn]],Times@@( #[[1]]^ #[[2]] &/@Partition[idn,2]),(Times@@(#[[1]]^#[[2]] &/@ Partition[ Most[idn],2]))Last[idn]]]; Array[ptm,70,0] (* _Harvey P. Dale_, Jul 15 2019 *)
%o A133500 (Haskell)
%o A133500 a133500 = train . reverse . a031298_row where
%o A133500    train []       = 1
%o A133500    train [x]      = x
%o A133500    train (u:v:ws) = u ^ v * (train ws)
%o A133500 -- _Reinhard Zumkeller_, May 27 2013
%o A133500 (Python)
%o A133500 def A133500(n):
%o A133500     s = str(n)
%o A133500     l = len(s)
%o A133500     m = int(s[-1]) if l % 2 else 1
%o A133500     for i in range(0,l-1,2):
%o A133500         m *= int(s[i])**int(s[i+1])
%o A133500     return m # _Chai Wah Wu_, Jun 16 2017
%Y A133500 Cf. A075877, A133501 (number of steps to reach fixed point), A133502, A135385 (the conjectured list of fixed points), A135384 (numbers which converge to 2592). For records see A133504, A133505; for the fixed points that are reached when this map is iterated starting at n, see A287877.
%Y A133500 Cf. also A133048 (powerback), A031346 and A003001 (persistence).
%Y A133500 Cf. also A031298, A007376.
%K A133500 nonn,base,look
%O A133500 0,3
%A A133500 _J. H. Conway_, Dec 03 2007