A394690 Smallest k such that k * n is a Belgian-0 number.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 3, 1, 1, 6, 1, 1, 1, 7, 1, 2, 1, 1, 3, 5, 1, 1, 6, 1, 3, 1, 1, 3, 3, 1, 1, 3, 1, 8, 1, 1, 5, 4, 1, 7, 1, 2, 3, 1, 1, 1, 2, 2, 6, 4, 1, 9, 1, 1, 3, 3, 1, 3, 3, 3, 1, 1, 1, 3, 2, 2, 2, 1, 2, 9, 1, 1, 3, 5, 1, 6, 4, 3, 1, 9, 1, 3, 5, 1, 2, 2, 2, 12, 4, 1, 1

Offset

1,14

Comments

A Belgian-0 number is a number belonging to the sequence obtained by cyclically adding its own digits starting from 0. This sequence provides the minimum multiplier k >= 1 required to transform n into a Belgian-0 number via M = k * n.

Links

Table of n, a(n) for n=1..100.

Example

a(14) = 3 because 3 * 14 = 42. The cyclic sum of the digits of 42 starting from 0 is: 0 -> 4 -> 6 -> 10 -> 12 -> 16 -> 18 -> 22 -> 24 -> 28 -> 30 -> 34 -> 36 -> 40 -> 42, which reaches 42, so 42 is a Belgian-0 number. No smaller multiplier k works for n = 14.
a(19) = 6 because 6 * 19 = 114. The cyclic sum of the digits of 114 starting from 0 (1+1+4=6 per cycle) reaches 114 after exactly 19 complete cycles.

Crossrefs

Cf. A106039 (Belgian-0 numbers).

Sequence in context: A341850 A341847 A200223 * A236228 A082391 A283977

Adjacent sequences: A394687 A394688 A394689 * A394691 A394692 A394693

Keyword

nonn,base,easy,look

Author

Davide Rotondo and Guido Avagliano, Jun 24 2026

Status

approved