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