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A067443 Smallest n-th power starting with 2.

%I A067443 #14 Apr 04 2025 22:30:42
%S A067443 2,25,27,256,243,262144,2187,256,262144,282475249,2048,244140625,
%T A067443 2541865828329,268435456,205891132094649,2821109907456,
%U A067443 232630513987207,262144,274877906944,278218429446951548637196401,2097152,2384185791015625,27368747340080916343
%N A067443 Smallest n-th power starting with 2.
%C A067443 Terms from _Robert G. Wilson v_.
%H A067443 Robert Israel, <a href="/A067443/b067443.txt">Table of n, a(n) for n = 1..703</a>
%p A067443 f:= proc(n) local x, y;
%p A067443   for x from 2 do
%p A067443     y:= x^n;
%p A067443     if floor(y/10^ilog10(y)) = 2 then return x^n fi
%p A067443   od
%p A067443 end proc:
%p A067443 map(f, [$1..50]); # _Robert Israel_, Apr 02 2025
%t A067443 a = {}; Do[k = 1; While[First[IntegerDigits[k^n]] != 2, k++ ]; a = Append[a, k^n], {n, 1, 25}]; a (* _Robert G. Wilson v_ *)
%o A067443 (Python)
%o A067443 def a(n):
%o A067443   r = 1
%o A067443   while str(r**n)[0] != '2': r += 1
%o A067443   return r**n
%o A067443 print([a(n) for n in range(1, 24)]) # _Michael S. Branicky_, Feb 25 2021
%Y A067443 Cf. A067442.
%K A067443 base,easy,nonn
%O A067443 1,1
%A A067443 _Amarnath Murthy_, Feb 05 2002