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%I #17 Sep 24 2019 18:39:43
%S 101,251,10001,18751,200001,4218751,100000001,74218751,10000000001,
%T 3574218751,1000000000001,163574218751,100000000000001,
%U 480163574218751,2000000000000001,6230163574218751,1000000000000000001
%N Least m ending in 1 such that m^n ends in a string of n 0's followed by the final 1.
%C From _Robert Israel_, Sep 24 2019: (Start)
%C a(n) = 10^(n+1)+1 if n and 10 are coprime.
%C a(5*k) = 2*10^(5*k)+1 if k and 10 are coprime. (End)
%H Robert Israel, <a href="/A085610/b085610.txt">Table of n, a(n) for n = 1..400</a>
%e We have a(4)=18751 because the latter is the shortest number whose fourth power ends in 00001; Actually,18751^4=123622560703200001.
%p f:= proc(n) local z,R;
%p if igcd(n,10)=1 then return 10^(n+1)+1 fi;
%p min(select(t -> t mod 10 = 1, map(rhs@op, {msolve(z^n=1, 10^(n+1))} minus {{z=1}})));
%p end proc:
%p map(f, [$1..30]); # _Robert Israel_, Sep 24 2019
%K nonn
%O 1,1
%A _Lekraj Beedassy_, Jul 08 2003
%E More terms from _Ray Chandler_, Nov 23 2003
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