A274971 Numbers k such that (x+1)^3 - x^3 = k*y^2 has integer solutions.

1, 7, 19, 31, 37, 43, 61, 67, 79, 91, 103, 127, 139, 151, 157, 163, 169, 199, 211, 217, 223, 247, 271, 283, 307, 313, 331, 343, 349, 367, 373, 379, 397, 403, 427, 439, 463, 469, 487, 499, 511, 523, 547, 553, 571, 577, 607, 613, 619, 631, 643, 661, 679, 691

Offset

1,2

Links

Ray Chandler, Table of n, a(n) for n = 1..10000

Dario A. Alpern, Quadratic two integer variable equation solver

Example

7 is in the sequence because, for instance, (167^3-166^3)/7 = 11881 = 109^2.

Mathematica

A004611=Select[Range[500], And@@(Mod[#, 3]==1&)/@(First/@FactorInteger[#])&]; Select[A004611, Reduce[x^2+3== 12*#*y^2, {x, y}, Integers]=!=False &] (* Ray Chandler, Jul 24 2016 *)

Crossrefs

Cf. A001921 (k=1), A144929 (k=7), A145124 (k=19), A145323 (k=31), A145700 (k=37), A145336 (k=43), A274972 (k=61), A145212 (k=67), A145309 (k=79), A145530 (k=91), A147530 (k=103), A145720 (k=127).

Cf. A003215 is a subsequence; A004611 contains this sequence.

Sequence in context: A352338 A109355 A272404 * A040045 A242476 A079021

Adjacent sequences: A274968 A274969 A274970 * A274972 A274973 A274974

Keyword

nonn

Author

Colin Barker, Jul 13 2016

Extensions

More terms using solver at Alpern link by Ray Chandler, Jul 23 2016

Status

approved