A362591 Discriminants D of the positive Pell equation x^2 - D*y^2 = 1, whose fundamental and all higher roots produce abc-triples a+b=c (or 1 + D*y^2 = x^2) with radical R(abc) < c.

2, 5, 7, 8, 12, 13, 14, 18, 20, 21, 27, 28, 29, 31, 32, 39, 41, 45, 46, 47, 48, 50, 52, 53, 54, 56, 60, 62, 63, 67, 69, 70, 72, 73, 74, 75, 77, 79, 80, 84, 85, 89, 92, 93, 96, 98, 103, 108, 109, 112, 113, 114, 116, 117, 122, 124, 125, 126, 127, 128, 135, 137, 139, 145, 147, 149, 150

Offset

1,1

Comments

These abc-triples are rare situations for triples of additively related pairwise relatively prime positive integers a + b = c, when radical R(abc) < c. Generally R(abc) > c; see Wikipedia.

Links

Janis Kuzmanis, Table of n, a(n) for n = 1..390

Janis Kuzmanis, On the origin of abc-triples, hal.science/hal-04044029v1.

Wikipedia, abc-conjecture.

Crossrefs

Similar sequence for the negative Pell's equation is A362592.

Sequence in context: A325441 A192111 A294635 * A032402 A299326 A280848

Adjacent sequences: A362588 A362589 A362590 * A362592 A362593 A362594

Keyword

nonn

Author

Janis Kuzmanis, Apr 26 2023

Extensions

More terms from Janis Kuzmanis, Nov 12 2023

Status

approved