A096683 Least k such that decimal representation of k*n contains only digits 0 and 4.

4, 2, 148, 1, 8, 74, 572, 5, 49382716, 4, 4, 37, 308, 286, 296, 25, 2612, 24691358, 2316, 2, 1924, 2, 19148, 185, 16, 154, 163127572, 143, 151876, 148, 14324, 125, 13468, 1306, 1144, 12345679, 12, 1158, 1036, 1, 1084, 962, 102428, 1, 98765432

Offset: 1

Author

Ray Chandler, Jul 12 2004

Keywords

• base
• nonn

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004290, A078241-A078248, A079339, A096681, A096682, A096684, A096685, A096686, A096687, A096688.

Programs

Mathematica

f[n_] := Block[{id = {0, 4}, k = 1}, While[ Union[ Join[id, IntegerDigits[k*n]]] != id, k++]; k]; Array[f, 100] (* or *)
id = {0, 7}; lst = Union[ FromDigits /@ Flatten[ Table[ Tuples[id, j], {j, 15}], 1]]; If[ lst[[1]] == 0, lst = Rest@ lst]; f[n_] := (Min[ Select[lst, Mod[#, n] == 0 &]]/n) /. Infinity -> 0; Array[f, 100] (* or *)
id = {0, 7}; lst = Union[ FromDigits /@ Flatten[ Table[ Tuples[id, j], {j, 15}], 1]]; If[ lst[[1]] == 0, lst = Rest@ lst]; f[n_] := (SelectFirst[lst, Mod[#, n] == 0 &, 0]/n); a = Array[f, 100] (* requires Mathematica v10 *) (* Robert G. Wilson v, Sep 26 2016 *)

Formula

a(n) = A078243(n)/n.