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A067442 a(1) = 1 and then smallest nontrivial n-th power starting with 1.

%I A067442 #29 Sep 08 2022 08:45:05
%S A067442 1,16,125,16,1024,15625,128,1679616,19683,1024,177147,16777216,
%T A067442 1594323,16384,14348907,152587890625,131072,101559956668416,
%U A067442 1162261467,1048576,10460353203,17592186044416,11920928955078125,16777216
%N A067442 a(1) = 1 and then smallest nontrivial n-th power starting with 1.
%C A067442 Terms from _Robert G. Wilson v_.
%H A067442 Robert Israel, <a href="/A067442/b067442.txt">Table of n, a(n) for n = 1..1007</a>
%p A067442 f:= proc(n) local x,y;
%p A067442   for x from 2 to 10 do
%p A067442     y:= x^n;
%p A067442     if floor(y/10^ilog10(y)) = 1 then return x^n fi
%p A067442   od
%p A067442 end proc:
%p A067442 f(1):= 1:
%p A067442 map(f, [$1..50]); # _Robert Israel_, Aug 13 2019
%t A067442 a = {}; Do[k = 2; While[First[IntegerDigits[k^n]] != 1, k++ ]; a = Append[a, k^n], {n, 2, 25}]; a (* _Robert G. Wilson v_ *)
%o A067442 (PARI) a(n) = {if (n==1, return (1)); k=2; while (! (ispower(k,n) && (digits(k)[1] == 1)), k++); k;} \\ _Michel Marcus_, Mar 18 2015
%o A067442 (Magma) m:=1; sol:=[1]; for n in [2..24] do k:=2; while Reverse(Intseq(k^n))[1] ne 1 do; k:=k+1;  end while; sol[m+1]:=k^n; m:=m+1; end for; sol; // _Marius A. Burtea_, Aug 15 2019
%o A067442 (Python)
%o A067442 print(1,1)
%o A067442 n = 1
%o A067442 while n < 20:
%o A067442     n, p = n+1, 2
%o A067442     s = str(p**n)
%o A067442     while s[0] != "1":
%o A067442         p = p+1
%o A067442         s = str(p**n)
%o A067442     print(n,p**n) # _A.H.M. Smeets_, Aug 16 2019
%K A067442 base,easy,nonn
%O A067442 1,2
%A A067442 _Amarnath Murthy_, Feb 05 2002