A369153 Numbers k such that gcd(2*k^7+1, 3*k^3+2) > 1.

435, 1598, 2761, 3924, 5087, 6250, 7413, 8576, 9739, 10902, 12065, 13228, 14391, 15554, 16717, 17880, 19043, 20206, 21369, 22532, 23695, 24858, 26021, 27184, 28347, 29510, 30673, 31836, 32999, 34162, 35325, 36488, 37651, 38814, 39977, 41140, 42303, 43466

Offset: 0

Author

Philippe Deléham, Jan 15 2024

Keywords

• nonn
• easy
• changed

Comments

This GCD is 1163 if k == 435 (mod 1163), or 1 otherwise.

Examples

			a(0) = 435, 2*435^7+1 = 5894606169966093751 and 3*435^3+2 = 246938627, gcd(5894606169966093751, 246938627) = 1163.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Programs

Mathematica

Table[435+n*1163,{n,0,37}] (* James C. McMahon, Jan 15 2024 *)
LinearRecurrence[{2,-1},{435,1598},40] (* Harvey P. Dale, Aug 31 2025 *)

Formula

a(n) = 435 + 1163*n.

a(n) = 2*a(n-1) - a(n-2).

G.f.: (435 + 728*x)/(1 - x)^2.