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

1,2

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

Prog

(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

Crossrefs

Cf. A252001 (carries required); A252023 (inverse), A252079 (fixed points), A251984, A167831.

Cf. A262604 (first differences).

Sequence in context: A357082 A360521 A320870 * A039697 A319131 A231566

Adjacent sequences: A252019 A252020 A252021 * A252023 A252024 A252025

Keyword

nonn,base

Author

Reinhard Zumkeller, Dec 12 2014

Status

approved