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URL: https://oeis.org/A374735

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A374735
a(n) is the least k > 0 such that n and k*n can be added without carries in decimal.
2
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
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
KEYWORD
nonn,base,easy
AUTHOR
Rémy Sigrist, Jul 18 2024
STATUS
approved