login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A145187 Continued cotangent recurrence a(n+1)=a(n)^3+3*a(n) with a(1)=13. 10
13, 2236, 11179326964, 1397162674037779847605429310236, 2727350312258670490076364505418491429134385511825631286349491134548728023756939667650354964 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..5.

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))]

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*)

CROSSREFS

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

Sequence in context: A161588 A221927 A013718 * A221896 A209468 A270872

Adjacent sequences:  A145184 A145185 A145186 * A145188 A145189 A145190

KEYWORD

nonn

AUTHOR

Artur Jasinski, Oct 03 2008

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 20 10:18 EST 2022. Contains 350471 sequences. (Running on oeis4.)