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A374736
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a(n) is the least number of the form k*n for some k > 0 that can be added to n without carries in decimal.
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2
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0, 1, 2, 3, 4, 10, 12, 21, 40, 90, 10, 11, 12, 13, 14, 30, 32, 51, 180, 380, 20, 21, 22, 23, 24, 50, 52, 162, 140, 870, 30, 31, 32, 33, 34, 140, 252, 111, 760, 1560, 40, 41, 42, 43, 44, 450, 230, 141, 240, 2450, 100, 102, 104, 106, 324, 110, 112, 342, 1740
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OFFSET
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0,3
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LINKS
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FORMULA
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a(10*n) = 10*a(n).
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EXAMPLE
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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) = 40.
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PROG
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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*n); ); ); }
(Python)
from itertools import count
s = list(map(int, str(n)[::-1]))
return next(k for k in count(n, n) if all(a+b<=9 for a, b in zip(s, map(int, str(k)[::-1])))) # Chai Wah Wu, Jul 19 2024
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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