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

0,3

Comments

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

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

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

Cf. A031298.

Sequence in context: A004427 A113230 A065881 * A214950 A373064 A054055

Adjacent sequences: A133045 A133046 A133047 * A133049 A133050 A133051

Keyword

nonn,base

Author

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

Status

approved