A374736 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.
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
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) = 40.
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*n); ); ); } -
Python
from itertools import count def A374736(n): 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