OFFSET
1,1
COMMENTS
Square roots of these numbers are quadratic irrationals and corresponding chain fraction representations are periodic: sqrt(10) = [3;{2,3}], sqrt(26) = [5;{2,5}], sqrt(65) = [8;{2,8}], ..., where {} is denoted a period (we write {6} == {2,3}).
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
EXAMPLE
a(1)=10 because 10 = 3^2 + 1 is squarefree.
a(2)=26 because 26 = 5^2 + 1 is squarefree.
a(3)=65 because 65 = 8^2 + 1 is squarefree.
MAPLE
ts_fn3:=proc(n) local i, tren, ans; ans:=[ ]: for i from 1 to n do tren := i^(2)+1: if (isprime(tren) = false and numtheory[mobius] (tren) <> 0 ) then ans:=[ op(ans), tren ]: fi od: RETURN(ans) end: ts_fn3(200);
MATHEMATICA
Select[Range[70]^2+1, CompositeQ[#] && SquareFreeQ[#] &] (* Amiram Eldar, Feb 22 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Jani Melik, Jan 18 2008
EXTENSIONS
Definition corrected by T. D. Noe, Sep 16 2008
STATUS
approved