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 A006487 Denominators of greedy Egyptian fraction for square root of 2. (Formerly M2962) 115
 1, 3, 13, 253, 218201, 61323543802, 5704059172637470075854, 178059816815203395552917056787722451335939040, 227569456678536847041583520060628448125647436561262746582115170178319521793841532532509636 (list; graph; refs; listen; history; text; internal format)
 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 Sequence in context: A111431 A015701 A220294 * A240618 A042823 A132560 Adjacent sequences:  A006484 A006485 A006486 * A006488 A006489 A006490 KEYWORD nonn AUTHOR EXTENSIONS a(8) from Manfred Scheucher, Aug 17 2015 STATUS approved

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