cp's OEIS Frontend

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

%I A252022 #17 May 22 2025 10:21:41
%S A252022 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,
%T A252022 25,32,26,33,34,35,41,27,42,36,43,44,45,50,19,60,28,51,37,52,46,53,
%U A252022 100,29,70,101,38,61,102,47,110,39,120,48,111,54,103,55,104
%N A252022 Lexicographically earliest permutation of the positive integers, such that no carry occurs when adjacent terms are added in decimal representation.
%C A252022 a(n+1) = smallest number, not occurring earlier, such that no carry occurs when adding it to a(n) in decimal arithmetic.
%H A252022 Reinhard Zumkeller, <a href="/A252022/b252022.txt">Table of n, a(n) for n = 1..10000</a>
%H A252022 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Carry.html">Carry</a>
%H A252022 Wikipedia, <a href="http://en.wikipedia.org/wiki/Carry_(arithmetic)">Carry (arithmetic)</a>
%H A252022 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A252022 (Haskell)
%o A252022 import Data.List (delete)
%o A252022 a252022 n = a252022_list !! (n-1)
%o A252022 a252022_list = 1 : f [1] (drop 2 a031298_tabf) where
%o A252022    f xs zss = g zss where
%o A252022      g (ds:dss) = if all (<= 9) $ zipWith (+) xs ds
%o A252022        then (foldr (\d v -> 10 * v + d) 0 ds) : f ds (delete ds zss)
%o A252022        else g dss
%o A252022 (Python)
%o A252022 A252022_list, l, s, b = [1], [1], 2, set()
%o A252022 for _ in range(10**3):
%o A252022     i = s
%o A252022     while True:
%o A252022         if i not in b:
%o A252022             li = [int(d) for d in str(i)[::-1]]
%o A252022             for x,y in zip(li,l):
%o A252022                 if x+y > 9:
%o A252022                     break
%o A252022             else:
%o A252022                 l = li
%o A252022                 b.add(i)
%o A252022                 A252022_list.append(i)
%o A252022                 while s in b:
%o A252022                     b.remove(s)
%o A252022                     s += 1
%o A252022                 break
%o A252022         i += 1 # _Chai Wah Wu_, Dec 14 2014
%Y A252022 Cf. A252001 (carries required); A252023 (inverse), A252079 (fixed points), A251984, A167831.
%Y A252022 Cf. A262604 (first differences).
%K A252022 nonn,base
%O A252022 1,2
%A A252022 _Reinhard Zumkeller_, Dec 12 2014