A367295 Numbers k such that 6 is the first digit of 2^k.

6, 16, 26, 36, 79, 89, 99, 109, 119, 129, 139, 182, 192, 202, 212, 222, 232, 275, 285, 295, 305, 315, 325, 335, 368, 378, 388, 398, 408, 418, 428, 471, 481, 491, 501, 511, 521, 564, 574, 584, 594, 604, 614, 624, 667, 677, 687, 697, 707, 717, 760, 770, 780, 790

Offset: 1

Author

Martin Renner, Nov 12 2023

Keywords

• nonn
• base

Comments

The asymptotic density of this sequence is log_10(7/6) = 0.066946...

Crossrefs

Cf. A000079, A067497, A067469, A172404, A367294, A363060, A330243, A367296, A097415.

Programs

Maple

x := 1:
L := []:
for n from 0 to 10^3 do
  if 6 <= x and x < 7 then
    L := [op(L), n]
  fi;
  x := 2*x;
  if x > 10 then
    x := (1/10)*x fi;
od:
L;

Mathematica

Select[Range[800], IntegerDigits[2^#][[1]] == 6 &] (* Amiram Eldar, Nov 12 2023 *)