A205531 - OEIS

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).

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: A062734 A336567 A361902 * A269246 A334566 A342270

Adjacent sequences: A205528 A205529 A205530 * A205532 A205533 A205534

KEYWORD

nonn

AUTHOR

M. F. Hasler, Jan 28 2012

STATUS

approved