A249626 a(0) = 0, a(n+1) = smallest number, not occurring earlier, containing the smallest of the least frequently occurring digits in all preceding terms.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 29, 30, 34, 35, 36, 37, 38, 39, 40, 45, 46, 47, 48, 49, 50, 56, 57, 58, 59, 60, 67, 68, 69, 70, 78, 79, 80, 89, 90, 100, 21, 31, 41, 51, 61, 71, 81, 91, 22, 32, 42

Offset

0,3

Comments

a(n) = A102823(n) for n <= 55;

not all numbers occur: all repunits (A002275) greater than 1 are missing; idea of proof: for n > 1 the digit 1 will never again be the smallest of least frequently occurring digits;

A249648 gives positions of terms containing a zero.

Links

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

Example

n = 11: digits 0 and 1 occur twice in {a(k): k=0..10}, all other digits exactly once, where 2 is the smallest; therefore a(11) must contain digit 2, and 12 is the smallest unused number containing 2, hence a(11) = 12.
n = 55: digits 0..9 occur exactly 10 times in {a(k): k=0..54}; therefore a(55) must contain digit 0, the smallest digit; a(55) = 100, as 100 is the smallest unused number containing 0;
n = 56: least occurring digits in {a(k): k=0..10} are 2..9 and 2 is the smallest; therefore a(56) must contain digit 2, and 21 is the smallest unused number containing 2, hence a(56) = 21.

Prog

(Haskell)
import Data.List (delete, group, sortBy); import Data.Function (on)
a249626 n = a249626_list !! n
a249626_list = f (zip [0, 0..] [0..9]) a031298_tabf where
   f acds@((_, dig):_) zss = g zss where
     g (ys:yss) = if dig `elem` ys
                     then y : f acds' (delete ys zss) else g yss
       where y = foldr (\d v -> 10 * v + d) 0 ys
             acds' = sortBy (compare `on` fst) $
                    addd (sortBy (compare `on` snd) acds)
                         (sortBy (compare `on` snd) $
                                 zip (map length gss) (map head gss))
             addd cds [] = cds
             addd []   _ = []
             addd ((c, d) : cds) yys'@((cy, dy) : yys)
                  | d == dy  = (c + cy, d) : addd cds yys
                  | otherwise = (c, d) : addd cds yys'
             gss = sortBy compare $ group ys

Crossrefs

Cf. A031298, A002275, A011540, A249648, A102823.

Sequence in context: A048737 A122260 A122254 * A102823 A179308 A247806

Adjacent sequences: A249623 A249624 A249625 * A249627 A249628 A249629

Keyword

nonn,look,base

Author

Reinhard Zumkeller, Nov 03 2014

Status

approved