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A073015
a(n) is such that 2 = sqrt(1+sqrt(1+sqrt(1+....sqrt(a(n))....))) where there are n sqrt's.
1
3, 4, 9, 64, 3969, 15745024, 247905749270529, 61457260521381894004129398784, 3776994870793005510047522464634252677140721938309041881089, 14265690253996672387291309349232388828298289458234016200317876247121873778287073518355813134107244701354409532063744
OFFSET
0,1
REFERENCES
Berndt and Rankin, "Ramanujan, letters and commentary", p. 275
Bruce Berndt, "Ramanujan's notebook", part II, Springer Verlag, pp. 107-112
FORMULA
a(n) = A003096(n) + 1.
EXAMPLE
2 = sqrt(1+sqrt(1+sqrt(64))) hence a(3)=64.
MATHEMATICA
a[0] = 3; a[n_] := a[n] = (a[n-1]-1)^2; Table[ a[n], {n, 0, 9}] (* Jean-François Alcover, Dec 14 2011, after Pari *)
NestList[(#-1)^2&, 3, 10] (* Harvey P. Dale, Feb 04 2012 *)
PROG
(PARI) a(n)=if(n<1, 3*(n==0), (a(n-1)-1)^2)
(Haskell)
a073015 n = a073015_list !! n
a073015_list = iterate (\x -> (x - 1) ^ 2) 3 -- Reinhard Zumkeller, Jul 16 2012
CROSSREFS
Cf. A003096.
Sequence in context: A225473 A015240 A032477 * A364376 A240546 A248003
KEYWORD
easy,nice,nonn
AUTHOR
Benoit Cloitre, Aug 03 2002
STATUS
approved