A251984 -id:A251984 - 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.

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

Reinhard Zumkeller, Dec 12 2014

a(n+1) = smallest number, not occurring earlier, such that no carry occurs when adding it to a(n) in decimal arithmetic.

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

Cf. A252001 (carries required); A252023 (inverse), A252079 (fixed points), A251984, A167831.

Cf. A262604 (first differences).

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

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

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

Original entry on oeis.org

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, 26, 25, 35, 36, 34, 37, 33, 38, 32, 48, 42, 49, 31, 59, 41, 60, 40, 61, 43, 47, 44, 46, 45, 55, 50, 51, 52, 53, 54, 56, 57, 58, 62, 63, 64, 65, 66, 67, 68, 69, 70

Offset: 1

Reinhard Zumkeller, Dec 12 2014

a(n+1) = smallest number, not occurring earlier, such that a carry occurs when adding it to a(n) in decimal arithmetic.

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

Cf. A252022 (no carries); A252002 (inverse), A252078 (fixed points), A251984, A167831.

Cf. A262703 (first differences).

import Data.List (delete)
a252001 n = a252001_list !! (n-1)
a252001_list = 1 : f [1] (drop 2 a031298_tabf) where
   f xs zss = g zss where
     g (ds:dss) = if any (> 9) $ zipWith (+) xs ds
       then (foldr (\d v -> 10 * v + d) 0 ds) : f ds (delete ds zss)
       else g dss

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.

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