A212074 Beach-Williams Pell numbers of type 2p (p prime).

3202, 3554, 6178, 6274, 6626, 7522, 8354, 9442, 9634, 12706, 12962, 14978, 15586, 16418, 16546, 18754, 19298, 22114, 24098, 24482

Offset

1,1

Comments

Consider the problem of finding all integers n such that the Pell equation x^2 - n*y^2 = -1 is solvable in integers x,y with y != 0. Beach and Williams found that there are 102662 such values of n in the range 1 <= n <= 10^6.

Of these, 3531 "exceptional" values of n were not predicted by a certain list of criteria given in their paper. These 3531 exceptional values fall into 10 classes given in sequences A212074-A212083.

References

Beach, B. D. and Williams, H. C., A numerical investigation of the Diophantine equation x^2-dy^2=-1. Proceedings of the Third Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1972), pp. 37-68. Florida Atlantic Univ., Boca Raton, Fla., 1972.

Links

Table of n, a(n) for n=1..20.

Crossrefs

Cf. A212074-A212083.

Sequence in context: A231203 A035777 A108001 * A023308 A171350 A251396

Adjacent sequences: A212071 A212072 A212073 * A212075 A212076 A212077

Keyword

nonn

Author

N. J. A. Sloane, Apr 30 2012

Status

approved