A133048 Powerback(n): reverse the decimal expansion of n, drop any leading zeros, then apply the powertrain map of A133500 to the resulting number.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 1, 4, 9, 16, 25, 36, 49, 64, 81, 3, 1, 8, 27, 64, 125, 216, 343, 512, 729, 4, 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, 5, 1, 32, 243, 1024, 3125, 7776, 16807, 32768, 59049, 6, 1, 64, 729, 4096, 15625, 46656, 117649

Offset: 0

Author

J. H. Conway and N. J. A. Sloane, Dec 31 2007

Keywords

• nonn
• base

Comments

a(A221221(n)) = A133500(A221221(n)) = A222493(n). - Reinhard Zumkeller, May 27 2013

Examples

			E.g. 240 -> (0)42 -> 4^2 = 16; 12345 -> 54321 -> 5^4*3^2*1 = 5625.
		

Links

• N. J. A. Sloane, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A131571 (fixed points), A133059 and A133134 (records); A133500 (powertrain).

Cf. A133144 (length of trajectory), A031346 and A003001 (persistence).

Cf. A031298.

Programs

Haskell

a133048 0 = 0
a133048 n = train $ dropWhile (== 0) $ a031298_row n where
   train []       = 1
   train [x]      = x
   train (u:v:ws) = u ^ v * (train ws)
-- Reinhard Zumkeller, May 27 2013

Maple

powerback:=proc(n) local a,i,j,t1,t2,t3;
if n = 0 then RETURN(0); fi;
t1:=convert(n, base, 10); t2:=nops(t1);
for i from 1 to t2 do if t1[i] > 0 then break; fi; od:
a:=1; t3:=t2-i+1;
for j from 0 to floor(t3/2)-1 do a := a*t1[i+2*j]^t1[i+2*j+1]; od:
if t3 mod 2 = 1 then a:=a*t1[t2]; fi;
RETURN(a); end;

Mathematica

ptm[n_]:=Module[{idn=IntegerDigits[IntegerReverse[n]]},If[ EvenQ[ Length[idn]],Times@@ (#[[1]]^#[[2]]&/@Partition[idn,2]),(Times@@(#[[1]]^#[[2]]&/@Partition[ Most[ idn],2]))Last[idn]]];Array[ptm,70,0] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 05 2020 *)