A229709 Least sum of two squares that is a primitive root of the n-th prime.

1, 2, 2, 5, 2, 2, 5, 2, 5, 2, 13, 2, 13, 5, 5, 2, 2, 2, 2, 13, 5, 29, 2, 13, 5, 2, 5, 2, 10, 5, 29, 2, 5, 2, 2, 13, 5, 2, 5, 2, 2, 2, 29, 5, 2, 34, 2, 5, 2, 10, 5, 13, 13, 18, 5, 5, 2, 26, 5, 13, 5, 2, 5, 17, 10, 2, 29, 10, 2, 2, 5, 13, 10, 2, 2, 5, 2, 5, 13

Offset

1,2

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..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

a(4) = 5 as 5 = 2^2 + 1^2 is a primitive root mod 7 (the 4th prime).

Prog

(Sage) def A229709(n) : p = nth_prime(n); return next(i for i in PositiveIntegers() if i%p!=0 and mod(i, p).multiplicative_order() == p-1 and all(q%4 != 3 or e%2==0 for (q, e) in factor(i)))

Crossrefs

Cf. A001481, A122028, A229710.

Sequence in context: A319771 A021448 A359246 * A242277 A241476 A309727

Adjacent sequences: A229706 A229707 A229708 * A229710 A229711 A229712

Keyword

nonn

Author

Eric M. Schmidt, Sep 27 2013

Status

approved