A252023 -id:A252023 - cp's OEIS frontend

A252079 Fixed points of permutations A252022 and A252023.

1, 2, 3, 4, 5, 36, 72, 125, 136, 900, 4454, 8021, 27223, 33905, 73222, 127536, 146353, 180177, 234668, 273241

Offset: 1

Reinhard Zumkeller, Dec 13 2014

Cf. A252022, A252023, A252078.

a252079 n = a252079_list !! (n-1)
a252079_list = [x | x <- [1..], a252022 x == x]

A252079_list, l, s, b = [1], [1], 2, set()
for n in range(2, 10**5):
    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)
                if i == n:
                    A252079_list.append(i)
                while s in b:
                    b.remove(s)
                    s += 1
                break
        i += 1 # Chai Wah Wu, Dec 14 2014

a(16)-a(20) from Chai Wah Wu, Dec 14 2014

A252022 Lexicographically earliest permutation of the positive integers, such that no carry occurs when adjacent terms are added in decimal representation.

Original entry on oeis.org

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

cp's OEIS Frontend

A252079 Fixed points of permutations A252022 and A252023.

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