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A144836 a(n) = Lucas(4^n). 4
2, 7, 2207, 23725150497407, 316837008400094222150776738483768236006420971486980607 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
Previous name: a(n) = round(phi^(4^n)) where phi is the golden ratio (A001622).
LINKS
FORMULA
a(n) = phi^(4^n) + (1 - phi)^(4^n) = phi^(4^n) + (-phi)^(-4^n), where phi is golden ratio = (1 + sqrt(5))/2 = 1.6180339887... . - Artur Jasinski, Oct 05 2008
a(n) = 2*cosh(4^n*arccosh(sqrt(5)/2)). - Artur Jasinski, Oct 09 2008
a(n+1) = a(n)^4 - 4*a(n-1)^2 + 2 with a(1) = 7. - Peter Bala, Nov 28 2022
MAPLE
a := proc(n) option remember; if n = 1 then 7 else a(n-1)^4 - 4*a(n-1)^2 + 2 end if; end proc: seq(a(n), n = 1..4); # Peter Bala, Nov 28 2022
MATHEMATICA
c = N[GoldenRatio, 1000]; Table[Round[c^(4^n)], {n, 0, 5}]
c = (1 + Sqrt[5])/2; Table[Expand[c^(4^n) + (1 - c)^(4^n)], {n, 0, 5}] (* Artur Jasinski, Oct 05 2008 *)
Table[Round[N[2*Cosh[4^n*ArcCosh[Sqrt[5]/2]], 100], {n, 1, 7}] (* Artur Jasinski, Oct 09 2008 *)
PROG
(PARI) a(n)=round(((1+sqrt(5))/2)^4^n) \\ Charles R Greathouse IV, Jul 29 2011
CROSSREFS
Sequence in context: A138198 A358482 A320505 * A174308 A088549 A226704
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Sep 22 2008
EXTENSIONS
Offset corrected by Charles R Greathouse IV, May 15 2013
Offset changed to 0 by Georg Fischer, Sep 02 2022
New name from Peter Bala, Nov 18 2022
STATUS
approved

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Last modified May 17 19:53 EDT 2024. Contains 372607 sequences. (Running on oeis4.)