A229710 Least m of maximal order mod n such that m is a sum of two squares.

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

Author

Eric M. Schmidt, Sep 27 2013

Keywords

• nonn

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).

Examples

			The integer 5 = 2^2 + 1^2 has order 2 mod 12, the maximum, so a(12) = 5.
		

Links

• Eric M. Schmidt, Table of n, a(n) for n = 5..10000
• 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.

Crossrefs

Cf. A001481, A111076, A229708, A229709.

Programs

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)))