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 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 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

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