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A274971 Numbers k such that (x+1)^3 - x^3 = k*y^2 has integer solutions. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

D. 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: A261338 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

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Last modified August 18 18:04 EDT 2017. Contains 290732 sequences.