cp's OEIS Frontend

A085610 Least m ending in 1 such that m^n ends in a string of n 0's followed by the final 1.

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