A334914 Least positive multiple of n that when written in base 10 uses only 0's, 1's, 2's and 3's.

1, 2, 3, 12, 10, 12, 21, 32, 333, 10, 11, 12, 13, 112, 30, 32, 102, 1332, 133, 20, 21, 22, 23, 120, 100, 130, 1323, 112, 203, 30, 31, 32, 33, 102, 210, 1332, 111, 1102, 312, 120, 123, 210, 301, 132, 3330, 230, 1222, 1200, 1323, 100, 102, 312, 212, 2322, 110

Offset: 1

Author

Bernard Schott, May 16 2020

Keywords

• nonn
• base

Comments

a(n) = n iff n is in A007090; there is no isolated fixed point because fixed points are always in patterns of 4 consecutive terms, and the first few patterns are (0,1,2,3), (10,11,12,13), (20,21,22,23), (30,31,32,33), (100,101,102,103) ...

Examples

			a(18) = 1332 because 1332 is the smallest multiple of 18 whose decimal digits are all 0, 1, 2 or 3.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004290 (similar, with digits 0 and 1), A181060 (similar, with digits 0, 1 and 2).

Programs

Maple

f:= proc(n) local k;
  for k from 1 do if convert(convert(k*n,base,10),set) subset {0,1,2,3} then return k*n fi od
end proc:
map(f, [$1..100]); # Robert Israel, May 18 2020

Mathematica

Table[SelectFirst[Rest @ Flatten [FromDigits /@ Tuples[Range[0, 3], 4]], Divisible[#, n] &], {n, 1, 55}] (* Amiram Eldar, May 16 2020 *)

PARI

a(n) = my(k=1); while(vecmax(digits(k*n))>3, k++); k*n \\ Michel Marcus, May 17 2020