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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).

%I A082568 #18 Oct 26 2022 16:11:50
%S A082568 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,
%T A082568 31,14,23,33,22,29,17,26,37,34,25,9,13,16,28,21,19,27,45,32,39,17,10,
%U A082568 49,35,25,29,53,21,38,15,37,24,57,53,50,11,40,61,55,63,44
%N A082568 First nontrivial square root of unity mod A033949(n), i.e., smallest x > 1 such that x^2 == 1 mod A033949(n).
%H A082568 Alois P. Heinz, <a href="/A082568/b082568.txt">Table of n, a(n) for n = 1..20000</a>
%e A082568 a(3) = 4 because A033949(3) = 15 and 4^2 = 16 == 1 mod 15 is the first integer to do so.
%o A082568 (PARI) for (n=3,100, for (j=2,n-2,if (j^2%n==1,print1(j","); break)))
%o A082568 (Python)
%o A082568 from itertools import chain, count, islice
%o A082568 from sympy.ntheory import sqrt_mod_iter
%o A082568 def A082568_gen(): # generator of terms
%o A082568     return chain.from_iterable((sorted(filter(lambda m:1<m<n-1,sqrt_mod_iter(1,n)))[:1] for n in count(2)))
%o A082568 A082568_list = list(islice(A082568_gen(),30)) # _Chai Wah Wu_, Oct 26 2022
%Y A082568 Cf. A033949.
%Y A082568 Column k=1 of A277776.
%K A082568 nonn
%O A082568 1,1
%A A082568 _Jon Perry_, May 06 2003
%E A082568 Offset corrected, name clarified and more terms from _Alois P. Heinz_, Oct 30 2016