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

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..9999

Eric Weisstein's World of Mathematics, Carry

Wikipedia, Carry (arithmetic)

Formula

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

Prog

(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

Crossrefs

Cf. A004151, A122840, A031298, A167832.

Sequence in context: A083824 A087029 A104348 * A298372 A089186 A055120

Adjacent sequences: A251981 A251982 A251983 * A251985 A251986 A251987

Keyword

nonn,base,look

Author

Reinhard Zumkeller, Dec 12 2014

Status

approved