A335401 - OEIS

%I #16 May 06 2022 13:13:51

%S 1,1,1,3,2,2,3,4,37,1,1,1,1,8,2,2,6,74,7,1,1,1,1,5,4,5,49,4,7,1,1,1,1,

%T 3,6,37,3,29,8,3,3,5,7,3,74,5,26,25,27,2,2,6,4,43,2,2,23,4,17,2,2,5,

%U 21,5,2,2,3,15,19,3,3,31,14,3,4,132,3,4,27,4,41

%N a(n) is the smallest positive number such that the decimal digits of n*a(n) are all 0, 1, 2 or 3.

%C If a(n) = k, then a(10n) = k.

%C a(n) = 1 iff n is in A007090; hence, except for a(1) = a(2) = a(3) = 1, the terms 1 always appear in strings of 4 consecutive 1's.

%C Records occur for n: 1, 4, 8, 9, 18, 76,  ...

%F a(n) = A334914(n)/n.

%e a(9)= 37 because 9*37=333 is the smallest multiple of 9 whose decimal digits are all 0, 1, 2 or 3.

%t a[n_] := Block[{k = 1}, While[Max@ IntegerDigits[k n] > 3, k++]; k]; Array[a, 81] (* _Giovanni Resta_, Jun 06 2020 *)

%o (PARI) a(n) = my(k=1); while(vecmax(digits(k*n))>3, k++); k; \\ _Michel Marcus_, Jun 08 2020

%Y Cf. A007090, A334914.

%Y Cf. A079339 (similar, with digits 0 and 1), A181061 (similar, with digits 0, 1 and 2).

%K nonn,base

%O 1,4

%A _Bernard Schott_, Jun 06 2020

%E More terms from _Giovanni Resta_, Jun 06 2020