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%I #14 Jul 22 2020 11:42:35
%S 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 25,32,26,33,34,35,41,27,42,36,43,44,45,50,19,60,28,51,37,52,46,53,
%U 100,29,70,101,38,61,102,47,110,39,120,48,111,54,103,55,104
%N Lexicographically earliest permutation of the positive integers, such that no carry occurs when adjacent terms are added in decimal representation.
%C a(n+1) = smallest number, not occurring earlier, such that no carry occurs when adding it to a(n) in decimal arithmetic.
%H Reinhard Zumkeller, <a href="/A252022/b252022.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Carry.html">Carry</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Carry_(arithmetic)">Carry (arithmetic)</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (Haskell)
%o import Data.List (delete)
%o a252022 n = a252022_list !! (n-1)
%o a252022_list = 1 : f [1] (drop 2 a031298_tabf) where
%o f xs zss = g zss where
%o g (ds:dss) = if all (<= 9) $ zipWith (+) xs ds
%o then (foldr (\d v -> 10 * v + d) 0 ds) : f ds (delete ds zss)
%o else g dss
%o (Python)
%o A252022_list, l, s, b = [1], [1], 2, set()
%o for _ in range(10**3):
%o ....i = s
%o ....while True:
%o ........if i not in b:
%o ............li = [int(d) for d in str(i)[::-1]]
%o ............for x,y in zip(li,l):
%o ................if x+y > 9:
%o ....................break
%o ............else:
%o ................l = li
%o ................b.add(i)
%o ................A252022_list.append(i)
%o ................while s in b:
%o ....................b.remove(s)
%o ....................s += 1
%o ................break
%o ........i += 1 # _Chai Wah Wu_, Dec 14 2014
%Y Cf. A252001 (carries required); A252023 (inverse), A252079 (fixed points), A251984, A167831.
%Y Cf. A262604 (first differences).
%K nonn,base
%O 1,2
%A _Reinhard Zumkeller_, Dec 12 2014
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