A374735 - OEIS

%I #16 Jul 19 2024 18:18:55

%S 1,1,1,1,1,2,2,3,5,10,1,1,1,1,1,2,2,3,10,20,1,1,1,1,1,2,2,6,5,30,1,1,

%T 1,1,1,4,7,3,20,40,1,1,1,1,1,10,5,3,5,50,2,2,2,2,6,2,2,6,30,60,2,2,2,

%U 2,5,2,2,3,15,70,3,3,3,7,3,4,12,13,40,80,5,5

%N a(n) is the least k > 0 such that n and k*n can be added without carries in decimal.

%H Rémy Sigrist, <a href="/A374735/b374735.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = 1 iff n belongs to A007091.

%F a(10*n) = a(n).

%e For n = 8:

%e - 1*8 = 8; computing 8 + 8 requires a carry,

%e - 2*8 = 16; computing 8 + 16 requires a carry,

%e - 3*8 = 24; computing 8 + 24 requires a carry,

%e - 4*8 = 32; computing 8 + 32 requires a carry,

%e - 5*8 = 40; computing 8 + 40 does not require a carry,

%e - so a(8) = 5.

%o (PARI) a(n, base = 10) = { for (k = 1, oo, if (sumdigits((k+1)*n, base) == sumdigits(n, base) + sumdigits(k*n, base), return (k););); }

%o (Python)

%o from itertools import count

%o def A374735(n):

%o     s = list(map(int,str(n)[::-1]))

%o     return next(k for k in count(1) if all(a+b<=9 for a, b in zip(s,map(int,str(k*n)[::-1])))) # _Chai Wah Wu_, Jul 19 2024

%Y Cf. A007091, A261891 (analog for binary), A353623 (analog for balanced ternary), A374736.

%K nonn,base,easy

%O 0,6

%A _Rémy Sigrist_, Jul 18 2024