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A367294
Numbers k such that 4 is the first digit of 2^k.
4
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
1,1
COMMENTS
The asymptotic density of this sequence is log_10(5/4) = 0.096910...
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 *)
KEYWORD
nonn,base
AUTHOR
Martin Renner, Nov 12 2023
STATUS
approved