

A205531


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).


4



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, 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, 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
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OFFSET

1,6


COMMENTS

Related to the 4.X Selfridge Conjecture by P. Underwood, which states that p is prime iff such a y exists.
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], ...


LINKS

Table of n, a(n) for n=1..132.
P. Underwood, 4.X Selfridge Conjecture (on "Prime Pages" profile), Jan 2012.


PROG

(PARI) A205531(n)=A205535(prime(n))


CROSSREFS

Sequence in context: A144209 A094544 A062734 * A269246 A330248 A247505
Adjacent sequences: A205528 A205529 A205530 * A205532 A205533 A205534


KEYWORD

nonn


AUTHOR

M. F. Hasler, Jan 28 2012


STATUS

approved



