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
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
Programs
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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
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