A073762 - OEIS

%I #43 Feb 28 2023 02:14:16

%S 12,36,60,84,108,132,156,180,204,228,252,276,300,324,348,372,396,420,

%T 444,468,492,516,540,564,588,612,636,660,684,708,732,756,780,804,828,

%U 852,876,900,924,948,972,996,1020,1044,1068,1092,1116,1140,1164,1188,1212

%N a(n) = 24*n - 12.

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

%C This is also the list of numbers n such that A259748(n)/n = 5/12. - _José María Grau Ribas_, Jul 12 2015.

%C 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

%H Vincenzo Librandi, <a href="/A073762/b073762.txt">Table of n, a(n) for n = 1..3000</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

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

%F a(n) = 24*n - 12. - _Max Alekseyev_, Mar 03 2007

%F a(n) = 12*A005408(n-1). - _Danny Rorabaugh_, Oct 22 2015

%F G.f.: 12*x*(1 + x)/(1 - x)^2. - _Ilya Gutkovskiy_, Apr 28 2016

%F Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/48. - _Amiram Eldar_, Feb 28 2023

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

%t 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}]

%t Range[12, 2000, 24] (* _Vladimir Joseph Stephan Orlovsky_, Jun 14 2011 *)

%o (PARI) a(n)=24*n-12 \\ _Charles R Greathouse IV_, Jun 14 2011

%o (PARI) x='x+O('x^100); Vec(12*(1+x)/(1-x)^2) \\ _Altug Alkan_, Oct 22 2015

%o (Magma) [24*n-12: n in [1..60]]; // _Vincenzo Librandi_, Jun 15 2011

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

%K nonn,easy

%O 1,1

%A _Labos Elemer_, Aug 08 2002