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A145504 a(n+1)=a(n)^2+2*a(n)-2 and a(1)=4 3
4, 22, 526, 277726, 77132286526, 5949389624883225721726, 35395236908668169265765137996816180039862526, 1252822795820745419377249396736955608088527968701950139470082687906021780162741058825726 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
General formula for a(n+1)=a(n)^2+2*a(n)-2 and a(1)=k+1 is a(n)=Floor[((k + Sqrt[k^2 + 4])/2)^(2^((n+1) - 1))
The next term (a(9)) has 175 digits. - Harvey P. Dale, Nov 16 2013
LINKS
FORMULA
From Peter Bala, Nov 12 2012: (Start)
a(n) = alpha^(2^(n-1)) + (1/alpha)^(2^(n-1)) - 1, where alpha := 1/2*(5 + sqrt(21)).
a(n) = A003487(n-1) - 1.
Recurrence: a(n) = 6*{product {k = 1..n-1} a(k)} - 2 with a(1) = 4.
Product {n = 1..inf} (1 + 1/a(n)) = 2/7*sqrt(21).
Product {n = 1..inf} (1 + 2/(a(n) + 1)) = sqrt(7/3).
(End)
MATHEMATICA
NestList[#^2+2#-2&, 4, 7] (* Harvey P. Dale, Nov 16 2013 *)
CROSSREFS
Sequence in context: A053722 A336212 A276122 * A321604 A276124 A104166
KEYWORD
nonn
AUTHOR
Artur Jasinski, Oct 11 2008
EXTENSIONS
One additional term (a(8)) from Harvey P. Dale, Nov 16 2013
STATUS
approved

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Last modified September 7 11:06 EDT 2024. Contains 375730 sequences. (Running on oeis4.)