

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.


35



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, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 1, 4, 16, 64, 256, 1024, 4096, 16384, 65536, 262144, 1, 5, 25, 125, 625, 3125, 15625, 78125, 390625, 1953125, 1, 6, 36, 216, 1296
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OFFSET

0,3


COMMENTS

We take 0^0 = 1.
For 1digit or 2digit numbers this is the same as A075877.  R. J. Mathar, Mar 28 2012


LINKS

N. J. A. Sloane, Three (No, 8) Lovely Problems from the OEIS, Experimental Mathematics Seminar, Rutgers University, Oct 05 2017, Part I, Part 2, Slides. (Mentions this sequence)


EXAMPLE

20 > 2^0 = 1,
21 > 2^1 = 2,
24 > 2^4 = 16,
39 > 3^9 = 19683,
623 > 6^2*3 = 108,
etc.


MAPLE

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[t22*i]^t1[t22*i1]; od: if t2 mod 2 = 1 then a:=a*t1[1]; fi; RETURN(n2*a); end; # N. J. A. Sloane, Dec 03 2007


MATHEMATICA

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 *)


PROG

(Haskell)
a133500 = train . reverse . a031298_row where
train [] = 1
train [x] = x
train (u:v:ws) = u ^ v * (train ws)
(Python)
s = str(n)
l = len(s)
m = int(s[1]) if l % 2 else 1
for i in range(0, l1, 2):
m *= int(s[i])**int(s[i+1])


CROSSREFS

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.


KEYWORD



AUTHOR



STATUS

approved



