A284379 Numbers k with digits 3 and 5 only.

3, 5, 33, 35, 53, 55, 333, 335, 353, 355, 533, 535, 553, 555, 3333, 3335, 3353, 3355, 3533, 3535, 3553, 3555, 5333, 5335, 5353, 5355, 5533, 5535, 5553, 5555, 33333, 33335, 33353, 33355, 33533, 33535, 33553, 33555, 35333, 35335, 35353, 35355, 35533, 35535

Offset: 1

Author

Jaroslav Krizek, Mar 26 2017

Keywords

• nonn
• base

Comments

Prime terms are in A020462.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Numbers n with digits 5 and k only for k = 0 - 4 and 6 - 9: A169964 (k = 0), A276037 (k = 1), A072961 (k = 2), this sequence (k = 3), A256290 (k = 4), A256291 (k = 6), A284380 (k = 7), A284381 (k = 8), A284382 (k = 9).

Programs

Magma

[n: n in [1..100000] | Set(IntegerToSequence(n, 10)) subset {3, 5}];

Maple

A:= 3,5: B:= [3,5];
for i from 1 to 5 do
  B:= map(t -> (10*t+3,10*t+5), B);
  A:= A, op(B);
od:
A; # Robert Israel, Apr 13 2020

Mathematica

Select[Range[35600], Times @@ Boole@ Map[MemberQ[{3, 5}, #] &, IntegerDigits@ #] > 0 &] (* or *)
Table[FromDigits /@ Union@ Apply[Join, Map[Permutations@ # &, Tuples[{3, 5}, n]]], {n, 5}] // Flatten (* Michael De Vlieger, Mar 27 2017 *)

Formula

From Robert Israel, Apr 13 2020: (Start)

a(n) = 2*A007931(n)+A002275(n).

a(2n+1) = 10*a(n)+3.

a(2n+2) = 10*a(n)+5.

G.f. g(x) satisfies g(x) = 10*(x^2+x)*g(x^2) + (3*x+5*x^2)/(1-x^2). (End)