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

1,1

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)

Links

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

Example

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

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

Crossrefs

Sequence in context: A165379 A127348 A061191 * A142530 A033241 A140021

Adjacent sequences: A085607 A085608 A085609 * A085611 A085612 A085613

Keyword

nonn

Author

Lekraj Beedassy, Jul 08 2003

Extensions

More terms from Ray Chandler, Nov 23 2003

Status

approved