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

1,2

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) ...

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A112979 A225723 A092972 * A261576 A081526 A075711

Adjacent sequences: A334911 A334912 A334913 * A334915 A334916 A334917

Keyword

nonn,base

Author

Bernard Schott, May 16 2020

Status

approved