A004284 Least positive multiple of n written in base 4 using only 0 and 1.

1, 10, 111, 10, 11, 1110, 111, 100, 1101, 110, 11111, 1110, 1001, 1110, 111111, 100, 101, 11010, 100111, 110, 111, 111110, 1011, 11100, 11011, 10010, 1101, 1110, 10011, 1111110, 11111, 1000, 101001, 1010, 111111, 11010, 1001111, 1001110, 10101, 1100, 100001

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000 (first 200 terms from Harvey P. Dale)

Example

   n | multiplier m | a(n) = m*n
  ---+--------------+------------
   1 |       1      |  1 =    1_4
   2 |       2      |  4 =   10_4
   3 |       7      | 21 =  111_4
   4 |       1      |  4 =   10_4
   5 |       1      |  5 =   11_4
   6 |      14      | 84 = 1110_4
   7 |       3      | 21 =  111_4
   8 |       2      | 16 =  100_4
   9 |       9      | 81 = 1101_4
  10 |       2      | 20 =  110_4

Maple

N:= 100: # for a(1) .. a(N)
V:= Vector(N): count:= 0:
for x from 1 while count < N do
  L:= convert(x, base, 2);
  y:= add(L[i]*4^(i-1), i=1..nops(L));
  for z in NumberTheory:-Divisors(y) do
    if z <= N and V[z] = 0 then V[z]:= add(L[i]*10^(i-1), i=1..nops(L)); count:= count+1 fi
  od;
od:
convert(V, list); # Robert Israel, Jan 01 2026

Mathematica

lpm4[n_]:=Module[{k=1}, While[Rest[Most[DigitCount[n k, 4]]]!={0, 0}, k++]; FromDigits[IntegerDigits[n k, 4]]]; Array[lpm4, 40] (* Harvey P. Dale, Dec 22 2012 *)

Crossrefs

Sequence in context: A282412 A282679 A086996 * A119484 A281749 A282364

Adjacent sequences: A004281 A004282 A004283 * A004285 A004286 A004287

Keyword

nonn,base

Author

David W. Wilson

Status

approved