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A357099 Second nontrivial square root of unity mod A033949(n), i.e., second smallest x > 1 such that x^2 == 1 mod the n-th positive integer that does not have a primitive root.

%I A357099 #38 Oct 26 2022 16:11:38
%S A357099 5,7,11,9,11,13,7,15,19,17,23,29,19,25,11,29,23,26,17,35,27,34,15,37,
%T A357099 19,55,33,51,43,35,47,41,19,49,39,43,53,31,29,69,59,23,71,64,47,61,56,
%U A357099 31,89,51,67,27,34,55,89,73,41,77,91,59,64,69,19,83,63,71
%N A357099 Second nontrivial square root of unity mod A033949(n), i.e., second smallest x > 1 such that x^2 == 1 mod the n-th positive integer that does not have a primitive root.
%H A357099 Alois P. Heinz, <a href="/A357099/b357099.txt">Table of n, a(n) for n = 1..20000</a>
%o A357099 (Python)
%o A357099 from itertools import count, chain, islice
%o A357099 from sympy.ntheory import sqrt_mod_iter
%o A357099 def A357099_gen(): # generator of terms
%o A357099     return chain.from_iterable((sorted(filter(lambda m:1<m<n-1,sqrt_mod_iter(1,n)))[1:2] for n in count(2)))
%o A357099 A357099_list = list(islice(A357099_gen(),30)) # _Chai Wah Wu_, Oct 26 2022
%Y A357099 Column k=2 of A277776.
%Y A357099 Cf. A033949, A082568.
%K A357099 nonn
%O A357099 1,1
%A A357099 _Alois P. Heinz_, Oct 25 2022