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A362100 Numbers k such that 8^k starts with k.

%I A362100 #10 Jul 09 2025 05:01:11
%S A362100 4,10,18,652,1299,8225,12949,56230,156277,3227298,144225157
%N A362100 Numbers k such that 8^k starts with k.
%p A362100 filter:= proc(n) local d1, d2, t;
%p A362100   t:= 8^n;
%p A362100   d1:= ilog10(t);
%p A362100   d2:= ilog10(n);
%p A362100   floor(t/10^(d1-d2)) = n
%p A362100 end proc:
%p A362100 select(filter, [$1..10^5]); # _Robert Israel_, Apr 10 2023
%o A362100 (Python)
%o A362100 from itertools import count, islice
%o A362100 def A362100_gen(startvalue=1): # generator of terms >= startvalue
%o A362100     a = 1<<3*(m:=max(startvalue,1))
%o A362100     for n in count(m):
%o A362100         if (s:=str(n))==str(a)[:len(s)]:
%o A362100             yield n
%o A362100         a <<= 3
%o A362100 A362100_list = list(islice(A362100_gen(),5)) # _Chai Wah Wu_, Apr 10 2023
%Y A362100 For k such that b^k starts with n, for b = 2,..., 9, see A100129, A362096, A320930, A362097-A362101.
%K A362100 nonn,base,more
%O A362100 1,1
%A A362100 _N. J. A. Sloane_, Apr 10 2023, based on an email from _Keith F. Lynch_