A073015 a(n) is such that 2 = sqrt(1+sqrt(1+sqrt(1+....sqrt(a(n))....))) where there are n sqrt's.

3, 4, 9, 64, 3969, 15745024, 247905749270529, 61457260521381894004129398784, 3776994870793005510047522464634252677140721938309041881089, 14265690253996672387291309349232388828298289458234016200317876247121873778287073518355813134107244701354409532063744

Offset: 0

Author

Benoit Cloitre, Aug 03 2002

Keywords

• easy
• nice
• nonn

Examples

			2 = sqrt(1+sqrt(1+sqrt(64))) hence a(3)=64.
		

References

• Berndt and Rankin, "Ramanujan, letters and commentary", p. 275
• Bruce Berndt, "Ramanujan's notebook", part II, Springer Verlag, pp. 107-112

Crossrefs

Cf. A003096.

Programs

Haskell

a073015 n = a073015_list !! n
a073015_list = iterate (\x -> (x - 1) ^ 2) 3  -- Reinhard Zumkeller, Jul 16 2012

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 *)

PARI

a(n)=if(n<1,3*(n==0),(a(n-1)-1)^2)

Formula

a(n) = A003096(n) + 1.