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%I #16 Nov 13 2023 07:32:29
%S 3,13,23,33,43,106,116,126,136,146,199,209,219,229,239,302,312,322,
%T 332,342,395,405,415,425,435,498,508,518,528,538,591,601,611,621,631,
%U 684,694,704,714,724,787,797,807,817,827,880,890,900,910,920,983,993,1003
%N Numbers k such that 8 is the first digit of 2^k.
%C The asymptotic density of this sequence is log_10(9/8) = 0.051152...
%p x := 1:
%p L := []:
%p for n from 0 to 10^3 do
%p if 8 <= x and x < 9 then
%p L := [op(L), n]
%p fi;
%p x := 2*x;
%p if x > 10 then
%p x := (1/10)*x fi;
%p od:
%p L;
%t Select[Range[1010], IntegerDigits[2^#][[1]] == 8 &] (* _Amiram Eldar_, Nov 12 2023 *)
%o (Python)
%o from itertools import islice
%o def A367296_gen(): # generator of terms
%o a, b, c, l = 8, 9, 1, 0
%o while True:
%o if a<=c:
%o if c<b:
%o yield l
%o a *= 10
%o b *= 10
%o c <<= 1
%o l += 1
%o A367296_list = list(islice(A367296_gen(),30)) # _Chai Wah Wu_, Nov 13 2023
%Y Cf. A000079, A067497, A067469, A172404, A367294, A363060, A367295, A330243, A097415.
%K nonn,base
%O 1,1
%A _Martin Renner_, Nov 12 2023
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