A252022 Lexicographically earliest permutation of the positive integers, such that no carry occurs when adjacent terms are added in decimal representation.

1, 2, 3, 4, 5, 10, 6, 11, 7, 12, 13, 14, 15, 20, 8, 21, 16, 22, 17, 30, 9, 40, 18, 31, 23, 24, 25, 32, 26, 33, 34, 35, 41, 27, 42, 36, 43, 44, 45, 50, 19, 60, 28, 51, 37, 52, 46, 53, 100, 29, 70, 101, 38, 61, 102, 47, 110, 39, 120, 48, 111, 54, 103, 55, 104

Offset: 1

Author

Reinhard Zumkeller, Dec 12 2014

Keywords

• nonn
• base

Comments

a(n+1) = smallest number, not occurring earlier, such that no 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. A252001 (carries required); A252023 (inverse), A252079 (fixed points), A251984, A167831.

Cf. A262604 (first differences).

Programs

Haskell

import Data.List (delete)
a252022 n = a252022_list !! (n-1)
a252022_list = 1 : f [1] (drop 2 a031298_tabf) where
   f xs zss = g zss where
     g (ds:dss) = if all (<= 9) $ zipWith (+) xs ds
       then (foldr (\d v -> 10 * v + d) 0 ds) : f ds (delete ds zss)
       else g dss

Python

A252022_list, l, s, b = [1], [1], 2, set()
for _ in range(10**3):
    i = s
    while True:
        if i not in b:
            li = [int(d) for d in str(i)[::-1]]
            for x,y in zip(li,l):
                if x+y > 9:
                    break
            else:
                l = li
                b.add(i)
                A252022_list.append(i)
                while s in b:
                    b.remove(s)
                    s += 1
                break
        i += 1 # Chai Wah Wu, Dec 14 2014