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A367296
Numbers k such that 8 is the first digit of 2^k.
4
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
1,1
COMMENTS
The asymptotic density of this sequence is log_10(9/8) = 0.051152...
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;
MATHEMATICA
Select[Range[1010], IntegerDigits[2^#][[1]] == 8 &] (* Amiram Eldar, Nov 12 2023 *)
PROG
(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 c<b:
yield l
a *= 10
b *= 10
c <<= 1
l += 1
A367296_list = list(islice(A367296_gen(), 30)) # Chai Wah Wu, Nov 13 2023
KEYWORD
nonn,base
AUTHOR
Martin Renner, Nov 12 2023
STATUS
approved