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A082568 First nontrivial square root of unity mod A033949(n), i.e., smallest x > 1 such that x^2 == 1 mod A033949(n). 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
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

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Last modified July 15 09:15 EDT 2024. Contains 374324 sequences. (Running on oeis4.)