A367296 Numbers k such that 8 is the first digit of 2^k.

3, 13, 23, 33, 43, 106, 116, 126, 136, 146, 199, 209, 219, 229, 239, 302, 312, 322, 332, 342, 395, 405, 415, 425, 435, 498, 508, 518, 528, 538, 591, 601, 611, 621, 631, 684, 694, 704, 714, 724, 787, 797, 807, 817, 827, 880, 890, 900, 910, 920, 983, 993, 1003

Offset: 1

Author

Martin Renner, Nov 12 2023

Keywords

• nonn
• base

Comments

The asymptotic density of this sequence is log_10(9/8) = 0.051152...

Links

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

Crossrefs

Cf. A000079, A067497, A067469, A172404, A367294, A363060, A367295, A330243, A097415.

Programs

Maple

x := 1:
L := []:
for n from 0 to 10^3 do
  if 8 <= x and x < 9 then
    L := [op(L), n]
  fi;
  x := 2*x;
  if x > 10 then
    x := (1/10)*x fi;
od:
L;
# alternative:
select(t -> floor(2^t/10^ilog10(2^t))=8, [$1..10^4]); # Robert Israel, Nov 12 2024

Mathematica

Select[Range[1010], IntegerDigits[2^#][[1]] == 8 &] (* Amiram Eldar, Nov 12 2023 *)

Python

from itertools import islice
def A367296_gen(): # generator of terms
    a, b, c, l = 8, 9, 1, 0
    while True:
        if a<=c:
            if cA367296_list = list(islice(A367296_gen(),30)) # Chai Wah Wu, Nov 13 2023