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A212074 Beach-Williams Pell numbers of type 2p (p prime). 10
3202, 3554, 6178, 6274, 6626, 7522, 8354, 9442, 9634, 12706, 12962, 14978, 15586, 16418, 16546, 18754, 19298, 22114, 24098, 24482 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 1 03:09 EST 2021. Contains 341732 sequences. (Running on oeis4.)