A145187 Continued cotangent recurrence a(n+1)=a(n)^3+3*a(n) with a(1)=13.

13, 2236, 11179326964, 1397162674037779847605429310236, 2727350312258670490076364505418491429134385511825631286349491134548728023756939667650354964

Offset: 1

Author

Artur Jasinski, Oct 03 2008

Keywords

• nonn

Comments

General formula for continued cotangent recurrences of the form a(n+1)=a(n)^3+3*a(n) with a(1)=k is a(n)=floor(((k+sqrt(k^2+4))/2)^(3^(n-1))).

For k=1 see A006267

k=2 see A006266

k=3 see A006268

k=4 see A006267(n+1)

k=5 see A006269

k=6 see A145180

k=7 see A145181

k=8 see A145182

k=9 see A145183

k=10 see A145184

k=11 see A145185

k=12 see A145186

k=13 see A145187

k=14 see A145188

k=15 see A145189

Crossrefs

Cf. A006267, A006266, A006268, A006269, A145180, A145181, A145182, A145183, A145184, A145185, A145186, A145187, A145188, A145189

Programs

Mathematica

a = {}; k = 13; Do[AppendTo[a, k]; k = k^3 + 3 k, {n, 1, 6}]; a
or
Table[Floor[((13 + Sqrt[173])/2)^(3^(n - 1))], {n, 1, 5}] (*Artur Jasinski*)

Formula

a(n+1)=a(n)^3+3*a(n) and a(1)=13

a(n)=Floor[((13+Sqrt[13^2+4])/2)^(3^(n-1))]