A082568 First nontrivial square root of unity mod A033949(n), i.e., smallest x > 1 such that x^2 == 1 mod A033949(n).

3, 5, 4, 7, 9, 8, 5, 13, 11, 15, 10, 6, 17, 14, 9, 13, 21, 19, 7, 16, 25, 21, 13, 20, 11, 8, 31, 14, 23, 33, 22, 29, 17, 26, 37, 34, 25, 9, 13, 16, 28, 21, 19, 27, 45, 32, 39, 17, 10, 49, 35, 25, 29, 53, 21, 38, 15, 37, 24, 57, 53, 50, 11, 40, 61, 55, 63, 44

Offset: 1

Author

Jon Perry, May 06 2003

Keywords

• nonn

Examples

			a(3) = 4 because A033949(3) = 15 and 4^2 = 16 == 1 mod 15 is the first integer to do so.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A033949.

Column k=1 of A277776.

Programs

PARI

for (n=3,100, for (j=2,n-2,if (j^2%n==1,print1(j","); break)))

Python

from itertools import chain, count, islice
from sympy.ntheory import sqrt_mod_iter
def A082568_gen(): # generator of terms
    return chain.from_iterable((sorted(filter(lambda m:1A082568_list = list(islice(A082568_gen(),30)) # Chai Wah Wu, Oct 26 2022

Extensions

Offset corrected, name clarified and more terms from Alois P. Heinz, Oct 30 2016