cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A073015 #18 Apr 11 2022 13:07:40
%S A073015 3,4,9,64,3969,15745024,247905749270529,61457260521381894004129398784,
%T A073015 3776994870793005510047522464634252677140721938309041881089,
%U A073015 14265690253996672387291309349232388828298289458234016200317876247121873778287073518355813134107244701354409532063744
%N A073015 a(n) is such that 2 = sqrt(1+sqrt(1+sqrt(1+....sqrt(a(n))....))) where there are n sqrt's.
%D A073015 Berndt and Rankin, "Ramanujan, letters and commentary", p. 275
%D A073015 Bruce Berndt, "Ramanujan's notebook", part II, Springer Verlag, pp. 107-112
%F A073015 a(n) = A003096(n) + 1.
%e A073015 2 = sqrt(1+sqrt(1+sqrt(64))) hence a(3)=64.
%t A073015 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 *)
%t A073015 NestList[(#-1)^2&,3,10] (* _Harvey P. Dale_, Feb 04 2012 *)
%o A073015 (PARI) a(n)=if(n<1,3*(n==0),(a(n-1)-1)^2)
%o A073015 (Haskell)
%o A073015 a073015 n = a073015_list !! n
%o A073015 a073015_list = iterate (\x -> (x - 1) ^ 2) 3  -- _Reinhard Zumkeller_, Jul 16 2012
%Y A073015 Cf. A003096.
%K A073015 easy,nice,nonn
%O A073015 0,1
%A A073015 _Benoit Cloitre_, Aug 03 2002