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%I #13 Apr 03 2023 10:36:12
%S 1,0,1,0,0,3,1,0,0,1,0,3,1,0,0,1,0,5,0,0,3,0,0,1,3,1,0,0,6,1,0,0,1,0,
%T 1,0,3,0,0,1,0,5,0,3,1,0,0,0,0,5,1,0,5,0,1,0,1,0,3,1,0,1,0,0,3,1,0,3,
%U 0,5,1,0,0,3,0,0,1,3,1,5,0,6,0,3,0,0,1,3,1,0,0,0,0,0,0,0,1,1,0,6,0,1,0,1,0,3,0,1,0,5,0,3,1,0,0,1,0,0,1,0,5,3,1,0,0,1,6,0,0,3,0,0
%N Least nonnegative integer y such that Kronecker(y^2 - 4, p(n)) == -1 and (x+2)^(p(n)+1) == 5 -+ 2*y (mod p(n), mod x^2 +- y*x + 1).
%C Related to the 4.X Selfridge Conjecture by P. Underwood, which states that p is prime iff such a y exists.
%C Records occur at [p=prime(k),y=a(k)] = [A205532(n), A205534(n)] = [2, 1], [13, 3], [61, 5], [109, 6], [1009, 9], [2689, 11], [8089, 15], [33049, 17], [53881, 21], [87481, 27], [483289, 29], [515761, 35], [1083289, 39], [3818929, 45], ...
%H P. Underwood, <a href="https://t5k.org/bios/page.php?id=181">4.X Selfridge Conjecture</a> (on "Prime Pages" profile), Jan 2012.
%o (PARI) A205531(n)=A205535(prime(n))
%K nonn
%O 1,6
%A _M. F. Hasler_, Jan 28 2012
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