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A144838 a(n) = round(phi^(6^n)) where phi = 1.6180339887498948482... = (sqrt(5)+1)/2. 4
18, 33385282, 1384619022984618483717737087933569992335566082 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

General (hyperbolic) trigonometric formula for a(n) = round(phi^((2k)^n)) = 2*cosh((2k)^n*arccosh(sqrt(5)/2) where phi = 1.6180339887498948482... = (sqrt(5)+1)/2. [From Artur Jasinski, Oct 09 2008]

LINKS

Table of n, a(n) for n=1..3.

FORMULA

a(n)=G^(6^n)+(1-G)^(6^n) = G^(6^n)+(-G)^(-6^n) where G is Golden ratio = (1+Sqrt[5])/2 = 1.618033989 [From Artur Jasinski, Oct 05 2008]

a(n)=2*Cosh[6^n*ArcCosh[Sqrt[5]/2] [From Artur Jasinski, Oct 09 2008]

MATHEMATICA

c = N[GoldenRatio, 1000]; Table[Round[c^(6^n)], {n, 1, 5}] (*Artur Jasinski*)

c = (1 + Sqrt[5])/2; Table[Expand[c^(6^n) + (1 - c)^(6^n)], {n, 0, 5}] [From Artur Jasinski, Oct 05 2008]

Table[Round[N[2*Cosh[6^n*ArcCosh[Sqrt[5]/2]], 100]], {n, 1, 4}] [From Artur Jasinski, Oct 09 2008]

CROSSREFS

Cf. A001566, A006267, A144836, A144837, A144838, A144839.

Sequence in context: A259164 A013808 A115479 * A013886 A259327 A271975

Adjacent sequences:  A144835 A144836 A144837 * A144839 A144840 A144841

KEYWORD

nonn,bref

AUTHOR

Artur Jasinski, Sep 22 2008

STATUS

approved

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Last modified March 28 06:09 EDT 2020. Contains 333073 sequences. (Running on oeis4.)