A251984 Smallest number such that a carry occurs when adding it to n in decimal representation.

9, 8, 7, 6, 5, 4, 3, 2, 1, 90, 9, 8, 7, 6, 5, 4, 3, 2, 1, 80, 9, 8, 7, 6, 5, 4, 3, 2, 1, 70, 9, 8, 7, 6, 5, 4, 3, 2, 1, 60, 9, 8, 7, 6, 5, 4, 3, 2, 1, 50, 9, 8, 7, 6, 5, 4, 3, 2, 1, 40, 9, 8, 7, 6, 5, 4, 3, 2, 1, 30, 9, 8, 7, 6, 5, 4, 3, 2, 1, 20, 9, 8, 7, 6

Offset: 1

Author

Reinhard Zumkeller, Dec 12 2014

Keywords

• nonn
• base
• look

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..9999
• Eric Weisstein's World of Mathematics, Carry
• Wikipedia, Carry (arithmetic)

Crossrefs

Cf. A004151, A122840, A031298, A167832.

Programs

Haskell

a251984 n = if d > 0 then 10 - d else 10 * a251984 n'
            where (n',d) = divMod n 10

Python

def a(n):
    s = str(n)
    t = s.strip('0')
    return (10 - int(t)%10) * 10**(len(s) - len(t))
print([a(n) for n in range(1, 85)]) # Michael S. Branicky, Sep 08 2021

Formula

a(n) = (10 - A004151(n) mod 10) * 10^A122840(n).