A145309 -id:A145309 - cp's OEIS frontend

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

Colin Barker, Jul 13 2016

nonn

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

Ray Chandler, Table of n, a(n) for n = 1..10000
Dario A. Alpern, Quadratic two integer variable equation solver

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.

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 *)

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

A145307 Numbers x such that there exists n in N : (x+79)^3-x^3=n^2.

Original entry on oeis.org

7663, 3514673818, 1603752710517223, 731795569310933239378, 333919781866113706302166783, 152368264304339620843780392200938, 69525943738264857888392566815788268343, 31724827179505362919884965402334038047270498

Offset: 1

Richard Choulet, Oct 06 2008

			a(1)=7663 because the first relation is : (7663+79)^3-7663^3=118579^2.

Index entries for linear recurrences with constant coefficients, signature (456303,-456303,1).

Cf. A145306.

LinearRecurrence[{456303,-456303,1},{7663,3514673818,1603752710517223},20] (* Harvey P. Dale, Dec 14 2017 *)

Vec(79*x*(-97-228151*x+98*x^2)/((x-1)*(x^2-456302*x+1)) + O(x^30)) \\ Colin Barker, Oct 18 2014

a(n+2) = 456302*a(n+1)-a(n)+18023850.
G.f.: 79*x*(-97-228151*x+98*x^2) / ( (x-1)*(x^2-456302*x+1) ). - R. J. Mathar, Nov 27 2011
a(n) = 79*A145309(n). - R. J. Mathar, Nov 27 2011

Editing and additional term a(8) from Colin Barker, Oct 18 2014

cp's OEIS Frontend

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

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