A059717 Start with decimal expansion of n; 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 add them; repeat.

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

Offset

0,3

Comments

a(A011557(n)) = 1; a(A059708(n)) = A059708(n). [Reinhard Zumkeller, Jul 05 2011]

Links

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

Example

For example, 59708 -> (0)8 + 597 = 605 -> 60 + 5 = 65 -> 6 + 5 = 11, stop, so a(59708) = 11.

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, 75}] (* Jean-François Alcover, May 31 2013 *)

Prog

(Haskell)
import Data.List (unfoldr)
a059717 n = if u == n || v == n then n else a059717 (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, Nov 16 2011 (corrected), Jul 05 2011

Crossrefs

Cf. A059707, A059708.

Sequence in context: A055483 A331472 A364362 * A004185 A068636 A328131

Adjacent sequences: A059714 A059715 A059716 * A059718 A059719 A059720

Keyword

nonn,base,easy,nice,look

Author

N. J. A. Sloane, Feb 08 2001

Status

approved