A252001 Lexicographically earliest permutation of the positive integers, such that a carry occurs when adjacent terms are added in decimal representation.

1, 9, 2, 8, 3, 7, 4, 6, 5, 15, 16, 14, 17, 13, 18, 12, 19, 11, 29, 21, 39, 22, 28, 23, 27, 24, 26, 25, 35, 36, 34, 37, 33, 38, 32, 48, 42, 49, 31, 59, 41, 60, 40, 61, 43, 47, 44, 46, 45, 55, 50, 51, 52, 53, 54, 56, 57, 58, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset

1,2

Comments

a(n+1) = smallest number, not occurring earlier, such that a carry occurs when adding it to a(n) in decimal arithmetic.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Carry

Wikipedia, Carry (arithmetic)

Index entries for sequences that are permutations of the natural numbers

Prog

(Haskell)
import Data.List (delete)
a252001 n = a252001_list !! (n-1)
a252001_list = 1 : f [1] (drop 2 a031298_tabf) where
   f xs zss = g zss where
     g (ds:dss) = if any (> 9) $ zipWith (+) xs ds
       then (foldr (\d v -> 10 * v + d) 0 ds) : f ds (delete ds zss)
       else g dss

Crossrefs

Cf. A252022 (no carries); A252002 (inverse), A252078 (fixed points), A251984, A167831.

Cf. A262703 (first differences).

Sequence in context: A343215 A137301 A299957 * A098784 A105172 A231533

Adjacent sequences: A251998 A251999 A252000 * A252002 A252003 A252004

Keyword

nonn,base

Author

Reinhard Zumkeller, Dec 12 2014

Status

approved