A374735 a(n) is the least k > 0 such that n and k*n can be added without carries in decimal.
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, 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, 2, 5, 2, 2, 3, 15, 70, 3, 3, 3, 7, 3, 4, 12, 13, 40, 80, 5, 5
Offset: 0
Examples
For n = 8: - 1*8 = 8; computing 8 + 8 requires a carry, - 2*8 = 16; computing 8 + 16 requires a carry, - 3*8 = 24; computing 8 + 24 requires a carry, - 4*8 = 32; computing 8 + 32 requires a carry, - 5*8 = 40; computing 8 + 40 does not require a carry, - so a(8) = 5.
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..10000
Programs
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PARI
a(n, base = 10) = { for (k = 1, oo, if (sumdigits((k+1)*n, base) == sumdigits(n, base) + sumdigits(k*n, base), return (k););); } -
Python
from itertools import count def A374735(n): s = list(map(int,str(n)[::-1])) 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
Formula
a(n) = 1 iff n belongs to A007091.
a(10*n) = a(n).