login
A229710
Least m of maximal order mod n such that m is a sum of two squares.
2
2, 5, 5, 5, 2, 13, 2, 5, 2, 5, 2, 5, 5, 5, 2, 13, 2, 13, 5, 5, 2, 37, 2, 5, 2, 13, 13, 5, 2, 5, 2, 5, 2, 13, 2, 13, 13, 5, 5, 13, 2, 5, 5, 5, 5, 13, 5, 37, 2, 5, 2, 5, 2, 37, 2, 13, 2, 13, 2, 5, 2, 5, 2, 5, 2, 17, 13, 5, 5, 5, 2, 13, 2, 37, 29, 13, 2, 13, 2, 5
OFFSET
5,1
COMMENTS
The sequence is undefined at n=4, as all the primitive roots are congruent to 3 mod 4.
Terms are not necessarily prime. For example, a(109) = 10.
a(prime(n)) = A229709(n).
LINKS
Christopher Ambrose, On the Least Primitive Root Expressible as a Sum of Two Squares, INTEGERS, Electronic J. of Combinatorial Number Theory, Vol. 13, Paper A55, 2013.
EXAMPLE
The integer 5 = 2^2 + 1^2 has order 2 mod 12, the maximum, so a(12) = 5.
PROG
(Sage) def A229710(n) : m = Integers(n).unit_group_exponent(); return 0 if n==1 else next(i for i in PositiveIntegers() if mod(i, n).is_unit() and mod(i, n).multiplicative_order() == m and all(p%4 != 3 or e%2==0 for (p, e) in factor(i)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric M. Schmidt, Sep 27 2013
STATUS
approved