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A145182 Continued cotangent recurrence a(n+1)=a(n)^3+3*a(n) and a(1)=8 11
8, 536, 153992264, 3651713626720249047672536, 48695646535829720063008633136610768101443687873746944465180200686293744264 (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 has 222 digits. - Harvey P. Dale, Mar 02 2018
LINKS
FORMULA
a(n+1)=a(n)3+3*a(n) and a(1)=8
a(n)=Floor[((8+Sqrt[8^2+4])/2)^(3^(n-1))]
MATHEMATICA
a = {}; k = 7; Do[AppendTo[a, k]; k = k^3 + 3 k, {n, 1, 6}]; a
or
Table[Floor[((8 + Sqrt[68])/2)^(3^(n - 1))], {n, 1, 5}] (*Artur Jasinski*)
RecurrenceTable[{a[1]==8, a[n]==a[n-1]^3+3a[n-1]}, a, {n, 5}] (* Harvey P. Dale, Mar 02 2018 *)
CROSSREFS
Sequence in context: A241367 A121740 A216353 * A089671 A112035 A200706
KEYWORD
nonn
AUTHOR
Artur Jasinski, Oct 03 2008
STATUS
approved

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Last modified June 20 16:01 EDT 2024. Contains 373526 sequences. (Running on oeis4.)