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A252001 Lexicographically earliest permutation of the positive integers, such that a carry occurs when adjacent terms are added in decimal representation.

%I A252001 #11 Feb 16 2025 08:33:24
%S A252001 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,
%T A252001 26,25,35,36,34,37,33,38,32,48,42,49,31,59,41,60,40,61,43,47,44,46,45,
%U A252001 55,50,51,52,53,54,56,57,58,62,63,64,65,66,67,68,69,70
%N A252001 Lexicographically earliest permutation of the positive integers, such that a carry occurs when adjacent terms are added in decimal representation.
%C A252001 a(n+1) = smallest number, not occurring earlier, such that a carry occurs when adding it to a(n) in decimal arithmetic.
%H A252001 Reinhard Zumkeller, <a href="/A252001/b252001.txt">Table of n, a(n) for n = 1..10000</a>
%H A252001 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Carry.html">Carry</a>
%H A252001 Wikipedia, <a href="http://en.wikipedia.org/wiki/Carry_(arithmetic)">Carry (arithmetic)</a>
%H A252001 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A252001 (Haskell)
%o A252001 import Data.List (delete)
%o A252001 a252001 n = a252001_list !! (n-1)
%o A252001 a252001_list = 1 : f [1] (drop 2 a031298_tabf) where
%o A252001    f xs zss = g zss where
%o A252001      g (ds:dss) = if any (> 9) $ zipWith (+) xs ds
%o A252001        then (foldr (\d v -> 10 * v + d) 0 ds) : f ds (delete ds zss)
%o A252001        else g dss
%Y A252001 Cf. A252022 (no carries); A252002 (inverse), A252078 (fixed points), A251984, A167831.
%Y A252001 Cf. A262703 (first differences).
%K A252001 nonn,base
%O A252001 1,2
%A A252001 _Reinhard Zumkeller_, Dec 12 2014