A251984 - OEIS

%I #11 Sep 08 2021 08:01:25

%S 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,

%T 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,

%U 3,2,1,30,9,8,7,6,5,4,3,2,1,20,9,8,7,6

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

%H Reinhard Zumkeller, <a href="/A251984/b251984.txt">Table of n, a(n) for n = 1..9999</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Carry.html">Carry</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Carry_(arithmetic)">Carry (arithmetic)</a>

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

%o (Haskell)

%o a251984 n = if d > 0 then 10 - d else 10 * a251984 n'

%o             where (n',d) = divMod n 10

%o (Python)

%o def a(n):

%o     s = str(n)

%o     t = s.strip('0')

%o     return (10 - int(t)%10) * 10**(len(s) - len(t))

%o print([a(n) for n in range(1, 85)]) # _Michael S. Branicky_, Sep 08 2021

%Y Cf. A004151, A122840, A031298, A167832.

%K nonn,base,look

%O 1,1

%A _Reinhard Zumkeller_, Dec 12 2014