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A145186 Continued cotangent recurrence a(n+1)=a(n)^3+3*a(n) and a(1)=12. 11
12, 1764, 5489037036, 165382092777963331246695013764, 4523404750894779548516344022127873154658656755028228436816797201835023951822441803129036 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
General formula for continued cotangent recurrences type:
a(n+1)=a(n)^3+3*a(n) and a(1)=k is following:
a(n)=Floor[((k+Sqrt[k^2+4])/2)^(3^(n-1))]
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
The next term (a(6)) has 263 digits. - Harvey P. Dale, May 21 2018
LINKS
FORMULA
a(n+1)=a(n)3+3*a(n) and a(1)=12.
a(n)=Floor[((12+Sqrt[12^2+4])/2)^(3^(n-1))].
MATHEMATICA
a = {}; k = 12; Do[AppendTo[a, k]; k = k^3 + 3 k, {n, 1, 6}]; a
or
Table[Floor[((12 + Sqrt[148])/2)^(3^(n - 1))], {n, 1, 5}] (*Artur Jasinski*)
NestList[#^3+3#&, 12, 5] (* Harvey P. Dale, May 21 2018 *)
CROSSREFS
Sequence in context: A252767 A015485 A174775 * A160304 A013479 A090914
KEYWORD
nonn
AUTHOR
Artur Jasinski, Oct 03 2008
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)