|
|
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
|
|
|
FORMULA
|
|
|
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 *)
|
|
PROG
|
(PARI) a(n)=if(n<1, 3*(n==0), (a(n-1)-1)^2)
(Haskell)
a073015 n = a073015_list !! n
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nice,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|