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A320930 Numbers k such that 4^k starts with k.

%I A320930 #15 Oct 20 2021 08:02:55
%S A320930 10,17,556,1771,4695,38537,56969,345797,141419115,1788191728
%N A320930 Numbers k such that 4^k starts with k.
%e A320930 4^10 = 1048576 starts with 10, so 10 is in the sequence.
%p A320930 filter:= proc(n) local t, b;
%p A320930   t:= 4^n;
%p A320930 b:= ilog10(t) - ilog10(n);
%p A320930 floor(t/10^b) = n
%p A320930 end proc:
%p A320930 select(filter, [$1..10^5]);
%o A320930 (Python)
%o A320930 def afind(limit, startk=1):
%o A320930     k, pow4 = startk, 4**startk
%o A320930     for k in range(startk, limit+1):
%o A320930         if str(pow4).startswith(str(k)):
%o A320930             print(k, end=", ")
%o A320930         pow4 *= 4
%o A320930 afind(10**4) # _Michael S. Branicky_, Oct 17 2021
%Y A320930 Cf. A000302, A100129, A288845.
%K A320930 nonn,base,more
%O A320930 1,1
%A A320930 _Robert Israel_, Oct 24 2018
%E A320930 a(8)-a(10) from _Giovanni Resta_, Oct 25 2018