A067442 - OEIS

%I #29 Sep 08 2022 08:45:05

%S 1,16,125,16,1024,15625,128,1679616,19683,1024,177147,16777216,

%T 1594323,16384,14348907,152587890625,131072,101559956668416,

%U 1162261467,1048576,10460353203,17592186044416,11920928955078125,16777216

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

%C Terms from _Robert G. Wilson v_.

%H Robert Israel, <a href="/A067442/b067442.txt">Table of n, a(n) for n = 1..1007</a>

%p f:= proc(n) local x,y;

%p   for x from 2 to 10 do

%p     y:= x^n;

%p     if floor(y/10^ilog10(y)) = 1 then return x^n fi

%p   od

%p end proc:

%p f(1):= 1:

%p map(f, [$1..50]); # _Robert Israel_, Aug 13 2019

%t 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 (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 (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 (Python)

%o print(1,1)

%o n = 1

%o while n < 20:

%o     n, p = n+1, 2

%o     s = str(p**n)

%o     while s[0] != "1":

%o         p = p+1

%o         s = str(p**n)

%o     print(n,p**n) # _A.H.M. Smeets_, Aug 16 2019

%K base,easy,nonn

%O 1,2

%A _Amarnath Murthy_, Feb 05 2002