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

1,1

Links

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

Example

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

Prog

(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:1<m<n-1, sqrt_mod_iter(1, n)))[:1] for n in count(2)))
A082568_list = list(islice(A082568_gen(), 30)) # Chai Wah Wu, Oct 26 2022

Crossrefs

Cf. A033949.

Column k=1 of A277776.

Sequence in context: A023859 A096457 A277897 * A242640 A210195 A069918

Adjacent sequences: A082565 A082566 A082567 * A082569 A082570 A082571

Keyword

nonn

Author

Jon Perry, May 06 2003

Extensions

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

Status

approved