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A006487
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Denominators of greedy Egyptian fraction for square root of 2.
(Formerly M2962)
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116
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1, 3, 13, 253, 218201, 61323543802, 5704059172637470075854, 178059816815203395552917056787722451335939040, 227569456678536847041583520060628448125647436561262746582115170178319521793841532532509636
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OFFSET
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0,2
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COMMENTS
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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
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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EXAMPLE
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MAPLE
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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:
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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