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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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Table of n, a(n) for n=0..9.

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-Fran├žois 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 * A240546 A248003 A063930

Adjacent sequences:  A073012 A073013 A073014 * A073016 A073017 A073018

KEYWORD

easy,nice,nonn

AUTHOR

Benoit Cloitre, Aug 03 2002

STATUS

approved

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Last modified August 19 03:10 EDT 2022. Contains 356216 sequences. (Running on oeis4.)