Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the 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