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Least number x such that x^n has n digits equal to k. Case k = 8.
2

%I #11 Jul 05 2023 18:35:23

%S 8,83,92,303,525,269,725,2169,1298,3466,867,1809,4624,793,7252,5195,

%T 7521,21397,11286,10482,19713,9573,15815,27879,20978,39673,53445,

%U 25276,30943,93984,39767,59441,92928,61256,84303,113117,145948,76304,109934,208709,92674,189862

%N Least number x such that x^n has n digits equal to k. Case k = 8.

%e a(4) = 303 because 303^4 = 8428892481 has 4 digits '8' and is the least number to have this property.

%p P:=proc(q,h) local a,j,k,n,t; for n from 1 to q do for k from 1 to q do

%p a:=convert(k^n,base,10); t:=0; for j from 1 to nops(a) do if a[j]=h then t:=t+1; fi; od;

%p if t=n then print(k); break; fi; od; od; end: P(10^9,8);

%t lnx[n_]:=Module[{x=1},While[DigitCount[x^n,10,8]!=n,x++];x]; Array[lnx,50] (* _Harvey P. Dale_, Jul 05 2023 *)

%K nonn,base,easy

%O 1,1

%A _Paolo P. Lava_, Apr 19 2017