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A085610
Least m ending in 1 such that m^n ends in a string of n 0's followed by the final 1.
2
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
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
KEYWORD
nonn
AUTHOR
Lekraj Beedassy, Jul 08 2003
EXTENSIONS
More terms from Ray Chandler, Nov 23 2003
STATUS
approved