A059707 If all digits have the same parity, stop; otherwise write down the number formed by the even digits and the number formed by the odd digits and multiply them; repeat.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 11, 2, 13, 4, 15, 6, 17, 8, 19, 20, 2, 22, 6, 24, 0, 26, 4, 28, 8, 0, 31, 6, 33, 2, 35, 8, 37, 24, 39, 40, 4, 42, 2, 44, 20, 46, 28, 48, 8, 0, 51, 0, 53, 20, 55, 0, 57, 40, 59, 60, 6, 62, 8, 64, 0, 66, 42, 68, 20, 0, 71, 4, 73, 28, 75, 42

Offset: 0

Author

N. J. A. Sloane, Feb 07 2001

Keywords

• nonn
• base
• easy
• nice
• look

Comments

a(A059708(n)) = A059708(n). - Reinhard Zumkeller, Jun 15 2012

Examples

			89 -> 8*9 = 72 -> 7*2 = 14 -> 1*4 = 4, stop, so a(89) = 4.
33278 -> 28*337 = 9436 -> 46*93 = 4278 -> 42*78 -> 2996 -> 26*99 = 2574 -> 24*57 = 1368 -> 68*13 = 884, stop, so a(33278) = 884.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A059708, A059717.

Programs

Haskell

import Data.List (unfoldr)
a059707 n = if u == n || v == n then n else a059707 (u * v) where
   (u,v) = foldl (\(x,y) d -> if odd d then (10*x+d,y) else (x,10*y+d))
        (0,0) $ reverse $ unfoldr
        (\z -> if z == 0 then Nothing else Just $ swap $ divMod z 10) n
-- Reinhard Zumkeller, Jun 15 2012

Mathematica

f[n_] := (id = IntegerDigits[n]; oddDigits = Select[id, OddQ]; evenDigits = Select[id, EvenQ]; Which[oddDigits == {}, FromDigits[evenDigits], evenDigits == {}, FromDigits[oddDigits], True, FromDigits[evenDigits] * FromDigits[oddDigits]]); a[n_] := FixedPoint[f, n]; Table[a[n], {n, 0, 76}] (* Jean-François Alcover, May 16 2013 *)
sp[n_]:=Module[{idn=IntegerDigits[n],e,o},e=Select[idn,EvenQ];o= Select[ idn,OddQ];If[Min[Length[o],Length[e]]>0,FromDigits[o] FromDigits[e], n]]; Table[FixedPoint[sp,i],{i,0,80}] (* Harvey P. Dale, Jun 05 2014 *)

Extensions

a(50) corrected by Reinhard Zumkeller, Jun 15 2012