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%I #30 Oct 27 2023 22:00:46
%S 2,10,16,23,30,37,44,52,59,67,75,83,92,100,109,117,126,135,144,153,
%T 162,171,180,190,199,208,218,227,237,247,256,266,276,286,296,306,316,
%U 326,336,346,356,367,377,387,398,408,418,429,439,450,460,471,482,492
%N a(n) = first k such that 2^k >= k^n, (for n >= 2, k >= 2).
%H Reinhard Zumkeller, <a href="/A054028/b054028.txt">Table of n, a(n) for n = 2..1000</a>
%e a(3) = 10 since 2^10=1024 >= 10^3=1000. a(4) = 16 since 2^16=65536 >= 16^4=65536.
%p Digits:= 500: f := k->2^x=x^k; seq(ceil(fsolve(f(n),x,2..infinity)), n=2..20); # for n >= 2
%t f[n_]:=Module[{k=2},While[2^k<k^n,k++];k]; Join[{0,0},Array[f,60,2]] (* _Harvey P. Dale_, Jan 15 2012 *)
%o (Haskell)
%o a054028 n = head [k | k <- [2..], 2^k >= k^n] :: Integer
%o -- _Reinhard Zumkeller_, Jul 24 2013
%Y Cf. A000079, A054029.
%K nonn,nice
%O 2,1
%A _Asher Auel_, Feb 28 2000