A394690 - OEIS

%I #41 Jun 29 2026 20:02:34

%S 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,

%T 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,

%U 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

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

%C 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.

%e 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.

%e 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.

%Y Cf. A106039 (Belgian-0 numbers).

%K nonn,base,easy,look

%O 1,14

%A _Davide Rotondo_ and _Guido Avagliano_, Jun 24 2026