A367294 Numbers k such that 4 is the first digit of 2^k.

2, 12, 22, 32, 42, 52, 62, 72, 82, 92, 105, 115, 125, 135, 145, 155, 165, 175, 185, 198, 208, 218, 228, 238, 248, 258, 268, 278, 288, 301, 311, 321, 331, 341, 351, 361, 371, 381, 394, 404, 414, 424, 434, 444, 454, 464, 474, 484, 497, 507, 517, 527, 537, 547

Offset: 1

Author

Martin Renner, Nov 12 2023

Keywords

• nonn
• base

Comments

The asymptotic density of this sequence is log_10(5/4) = 0.096910...

Crossrefs

Cf. A000079, A067497, A067469, A172404, A363060, A367295, A330243, A367296, A097415.

Programs

Maple

x := 1:
L := []:
for n from 0 to 10^3 do
  if 4 <= x and x < 5 then
    L := [op(L), n]
  fi;
  x := 2*x;
  if x > 10 then
    x := (1/10)*x fi;
od:
L;

Mathematica

Select[Range[550], IntegerDigits[2^#][[1]] == 4 &] (* Amiram Eldar, Nov 12 2023 *)