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

0,6

Links

Rémy Sigrist, Table of n, a(n) for n = 0..10000

Formula

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

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A153931 A214049 A273034 * A208437 A130377 A260956

Adjacent sequences: A374732 A374733 A374734 * A374736 A374737 A374738

Keyword

nonn,base,easy

Author

Rémy Sigrist, Jul 18 2024

Status

approved