A345702 Numbers that can be written as 2*a^2 - 1 and 3*b^3 - 1.

-1, 647, 41471, 472391, 2654207, 10124999, 30233087, 76236551, 169869311, 344373767, 647999999, 1147971527, 1934917631, 3127772231, 4879139327, 7381124999, 10871635967, 15641144711, 22039921151, 30485730887, 41471999999, 55576446407, 73470177791, 95927256071, 123834728447

Offset: 1

Author

Tanya Khovanova, Jun 24 2021

Keywords

• sign
• easy

Examples

			647 = 2*18^2 - 1 = 3*6^3 - 1. Thus, 647 is in this sequence.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Intersection of A056220 and A345701.

Programs

Mathematica

Intersection[Table[2 n^2 - 1, {n, 300000}], Table[3 n^3 - 1, {n, 100000}]]

Formula

G.f.: x*(647*x^6+36942*x^5+195681*x^4+195716*x^3+36921*x^2+654*x-1)/(1-x)^7. - Alois P. Heinz, Jun 24 2021

a(n) = 648*(n-1)^6 - 1 = 648*A001014(n-1) - 1. - Hugo Pfoertner, Jun 24 2021