A050275 Largest value c for Diophantine 1-triples (a,b,c) ordered by smallest c,b.

8, 12, 15, 16, 20, 21, 24, 24, 24, 28, 30, 32, 33, 35, 36, 39, 40, 40, 40, 42, 44, 45, 48, 48, 48, 51, 52, 55, 56, 56, 56, 57, 60, 60, 60, 63, 64, 65, 66, 68, 69, 70, 72, 72, 72, 75, 76, 77, 78, 80, 80, 80, 84, 84, 84, 85, 87, 88, 88, 88, 90, 91, 92, 93, 95, 96, 96, 96, 99

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Links

• Trajan Hammonds, Seoyoung Kim, Steven J. Miller, Arjun Nigam, Kyle Onghai, Dishant Saikia, and Lalit M. Sharma, k-Diophantine m-tuples in Finite Fields, arXiv:2201.06232 [math.NT], 2022.
• Eric Weisstein's World of Mathematics, Diophantus Property.

Crossrefs

Cf. A050273, A050274.

Programs

PARI

list(lim)=my(v=List()); for(b=8,lim, for(a=2,b-1, if(!issquare(a*b+1), next); for(c=1,a-1, if(issquare(a*c+1) && issquare(b*c+1), listput(v,b); next(2))))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2025