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A144836 a(n) = round(phi^(4^n)) where phi is the golden ratio. 4
2, 7, 2207, 23725150497407, 316837008400094222150776738483768236006420971486980607 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..5.

FORMULA

a(n)=G^(4^n)+(1-G)^(4^n) = G^(4^n)+(-G)^(-4^n) where G is Golden ratio = (1+Sqrt[5])/2 = 1.618033989 [From Artur Jasinski, Oct 05 2008]

a(n)=2*Cosh[4^n*ArcCosh[Sqrt[5]/2] [From Artur Jasinski, Oct 09 2008]

MATHEMATICA

c = N[GoldenRatio, 1000]; Table[Round[c^(4^n)], {n, 1, 5}] (*Artur Jasinski*)

c = (1 + Sqrt[5])/2; Table[Expand[c^(4^n) + (1 - c)^(4^n)], {n, 0, 5}] [From Artur Jasinski, Oct 05 2008]

Table[Round[N[2*Cosh[4^n*ArcCosh[Sqrt[5]/2]], 100], {n, 1, 7}][From Artur Jasinski, Oct 09 2008]

PROG

(PARI) a(n)=round(((1+sqrt(5))/2)^4^n) \\ Charles R Greathouse IV, Jul 29 2011

CROSSREFS

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

Sequence in context: A123180 A138198 A320505 * A174308 A088549 A226704

Adjacent sequences:  A144833 A144834 A144835 * A144837 A144838 A144839

KEYWORD

nonn

AUTHOR

Artur Jasinski, Sep 22 2008

EXTENSIONS

Offset corrected by Charles R Greathouse IV, May 15 2013

STATUS

approved

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Last modified April 5 08:04 EDT 2020. Contains 333238 sequences. (Running on oeis4.)