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A252022
Lexicographically earliest permutation of the positive integers, such that no carry occurs when adjacent terms are added in decimal representation.
8
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.
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
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Dec 12 2014
STATUS
approved