OFFSET
0,2
COMMENTS
Conjecture: Let a(n) = 2^2^(n + b(n)), then b(n) converges to a constant that is about 0.2163... - Manfred Scheucher, Aug 17 2015
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Manfred Scheucher, Table of n, a(n) for n = 0..11
Manfred Scheucher, Table of n, a(n) for n = 0..14
Manfred Scheucher, Sage Script.
D. S. Kluk and N. J. A. Sloane, Correspondence, 1979.
Eric Weisstein's World of Mathematics, Egyptian Fraction.
FORMULA
a(n) = ceiling(1/(sqrt(2) - Sum_{j=0..n-1} 1/a(j))). - Jon E. Schoenfield, Dec 26 2014
EXAMPLE
sqrt(2) = 1 + 1/3 + 1/13 + 1/253 + 1/218201 + ... . - Jon E. Schoenfield, Dec 26 2014
MAPLE
a[0]:= 1;
for n from 1 to 10 do
v:= ceil(1/(sqrt(2)-add(1/a[i], i=0..n-1)));
while not v::integer do
Digits:= 2*Digits;
v:= ceil(1/(sqrt(2)-add(1/a[i], i=0..n-1)))
od;
a[n]:= v;
od:
seq(a[i], i=0..10); # Robert Israel, Aug 17 2015
MATHEMATICA
lst={}; k=N[Sqrt[2], 1000]; Do[s=Ceiling[1/k]; AppendTo[lst, s]; k=k-1/s, {n, 12}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 02 2009 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(8) from Manfred Scheucher, Aug 17 2015
STATUS
approved