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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 Table of n, a(n) for n=1..5. 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 A006267, A006266, A006268, A006269, A145180, A145181, A145182, A145183, A145184, A145185, A145186, A145187, A145188, A145189 Sequence in context: A241367 A121740 A216353 * A089671 A112035 A200706 Adjacent sequences: A145179 A145180 A145181 * A145183 A145184 A145185 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.)