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

0,3

Links

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

Formula

a(n) = A374735(n) * n.

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

a(10*n) = 10*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) = 40.

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*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

Crossrefs

Cf. A007091, A261892 (analog for binary), A353624 (analog for balanced ternary), A374735.

Sequence in context: A276560 A339577 A049548 * A005456 A100773 A250112

Adjacent sequences: A374733 A374734 A374735 * A374738 A374739 A374740

Keyword

nonn,base,easy

Author

Rémy Sigrist, Jul 18 2024

Status

approved