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

101, 251, 10001, 18751, 200001, 4218751, 100000001, 74218751, 10000000001, 3574218751, 1000000000001, 163574218751, 100000000000001, 480163574218751, 2000000000000001, 6230163574218751, 1000000000000000001

Offset: 1

Author

Lekraj Beedassy, Jul 08 2003

Keywords

• nonn

Comments

From Robert Israel, Sep 24 2019: (Start)

a(n) = 10^(n+1)+1 if n and 10 are coprime.

a(5*k) = 2*10^(5*k)+1 if k and 10 are coprime. (End)

Examples

			We have a(4)=18751 because the latter is the shortest number whose fourth power ends in 00001; Actually,18751^4=123622560703200001.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..400

Programs

Maple

f:= proc(n) local z,R;
  if igcd(n,10)=1 then return 10^(n+1)+1 fi;
  min(select(t -> t mod 10 = 1, map(rhs@op, {msolve(z^n=1, 10^(n+1))} minus {{z=1}})));
end proc:
map(f, [$1..30]); # Robert Israel, Sep 24 2019

Extensions

More terms from Ray Chandler, Nov 23 2003