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

Author

Reinhard Zumkeller, Dec 12 2014

Keywords

• nonn
• base

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

Crossrefs

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

Cf. A262703 (first differences).

Programs

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