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

5,1

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

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.

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

Cf. A001481, A111076, A229708, A229709.

Sequence in context: A116698 A246900 A277086 * A240947 A023398 A186501

Adjacent sequences: A229707 A229708 A229709 * A229711 A229712 A229713

Keyword

nonn

Author

Eric M. Schmidt, Sep 27 2013

Status

approved