A073762 a(n) = 24*n - 12.

12, 36, 60, 84, 108, 132, 156, 180, 204, 228, 252, 276, 300, 324, 348, 372, 396, 420, 444, 468, 492, 516, 540, 564, 588, 612, 636, 660, 684, 708, 732, 756, 780, 804, 828, 852, 876, 900, 924, 948, 972, 996, 1020, 1044, 1068, 1092, 1116, 1140, 1164, 1188, 1212

Offset: 1

Author

Labos Elemer, Aug 08 2002

Keywords

• nonn
• easy

Comments

Previous name: "Smallest unrelated number belonging to a term of this sequence equals 8."

This is also the list of numbers k such that A259748(k)/k = 5/12. - José María Grau Ribas, Jul 12 2015.

Also the total number of line segments creating a stellated octahedron, where the length of each stellated edge equals n-1, and where the octahedron has 12 edges, each fixed at unit length. - Peter M. Chema, Apr 28 2016

Examples

			URSet[12] = {8,9,10} so 12 is here.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..3000
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A005408, A016825, A045763, A073758, A073759, A073760, A259748.

Programs

Magma

[24*n-12: n in [1..60]]; // Vincenzo Librandi, Jun 15 2011

Mathematica

tn[x_] := Table[w, {w, 1, x}]; di[x_] := Divisors[x]; dr[x_] := Union[di[x], rrs[x]]; rrs[x_] := Flatten[Position[GCD[tn[x], x], 1]]; unr[x_] := Complement[tn[x], dr[x]]; Do[s=Min[unr[n]]; If[Equal[s, 8], Print[n]], {n, 1, 1000}]
Range[12, 2000, 24] (* Vladimir Joseph Stephan Orlovsky, Jun 14 2011 *)

PARI

a(n)=24*n-12 \\ Charles R Greathouse IV, Jun 14 2011

PARI

x='x+O('x^100); Vec(12*(1+x)/(1-x)^2) \\ Altug Alkan, Oct 22 2015

Formula

Min{URS[m]} = 8, where UNR[m] = Complement[RRS[m], Divisors[m]].

a(n) = 24*n - 12. - Max Alekseyev, Mar 03 2007

a(n) = 12*A005408(n-1). - Danny Rorabaugh, Oct 22 2015

G.f.: 12*x*(1 + x)/(1 - x)^2. - Ilya Gutkovskiy, Apr 28 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/48. - Amiram Eldar, Feb 28 2023

From Elmo R. Oliveira, Apr 04 2025: (Start)

E.g.f.: 12*(exp(x)*(2*x - 1) + 1).

a(n) = 2*a(n-1) - a(n-2) for n > 2. (End)