Search: a013696 -id:a013696
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A013631
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Continued fraction for zeta(3).
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+10
31
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1, 4, 1, 18, 1, 1, 1, 4, 1, 9, 9, 2, 1, 1, 1, 2, 7, 1, 1, 7, 11, 1, 1, 1, 3, 1, 6, 1, 30, 1, 4, 1, 1, 4, 1, 3, 1, 2, 7, 1, 3, 1, 2, 2, 1, 16, 1, 1, 3, 3, 1, 2, 2, 1, 6, 1, 1, 1, 6, 1, 1, 4, 428, 5, 1, 1, 3, 1, 1, 11, 2, 4, 4, 5, 4, 1, 5, 14, 1, 3, 1, 2, 19, 1, 2, 5, 1, 7, 1, 1, 1, 1, 1, 57, 3, 2, 14, 2
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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EXAMPLE
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zeta(3) = 1.2020569031595942... = 1 + 1/(4 + 1/(1 + 1/(18 + 1/(1 + ...)))). - Harry J. Smith, Apr 20 2009
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MATHEMATICA
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ContinuedFraction[ Zeta[3], 100]
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PROG
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(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(zeta(3)); for (n=1, 20000, write("b013631.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 20 2009
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CROSSREFS
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KEYWORD
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nonn,cofr,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A013679
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Continued fraction for zeta(2) = Pi^2/6.
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+10
28
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1, 1, 1, 1, 4, 2, 4, 7, 1, 4, 2, 3, 4, 10, 1, 2, 1, 1, 1, 15, 1, 3, 6, 1, 1, 2, 1, 1, 1, 2, 2, 3, 1, 3, 1, 1, 5, 1, 2, 2, 1, 1, 6, 27, 20, 3, 97, 105, 1, 1, 1, 1, 1, 45, 2, 8, 19, 1, 4, 1, 1, 3, 1, 2, 1, 1, 1, 5, 1, 1, 2, 3, 6, 1, 1, 1, 2, 1, 5, 1, 1, 2, 9, 5, 3, 2, 1, 1, 1
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listen;
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OFFSET
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0,5
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 811.
David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 23.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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EXAMPLE
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1.644934066848226436472415166... = 1 + 1/(1 + 1/(1 + 1/(1 + 1/(4 + ...))))
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MATHEMATICA
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ContinuedFraction[ Pi^2/6, 100]
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PROG
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(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi^2/6); for (n=1, 20000, write("b013679.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 29 2009
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CROSSREFS
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KEYWORD
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nonn,cofr,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A013680
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Continued fraction for zeta(4).
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+10
23
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1, 12, 6, 1, 3, 1, 4, 183, 1, 1, 2, 1, 3, 1, 1, 5, 4, 2, 7, 23, 1, 1, 1, 1, 3, 2, 4, 2, 2, 22, 1, 13, 5, 1, 4, 2, 1, 3, 1, 1, 1, 6, 11, 40, 1, 7, 5, 2, 4, 1, 2, 3, 14, 9, 1, 33, 78, 1, 12, 4, 1, 2, 551, 1, 1, 1, 1, 1, 1, 2, 1, 9, 2, 7, 3, 1, 3, 2, 15, 1, 1, 2, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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EXAMPLE
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zeta(4) = 1 + 1/(12 + 1/(6 + 1/(1 + 1/(3 + ...)))). - Harry J. Smith, Apr 29 2009
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MATHEMATICA
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PROG
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(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi^4/90); for (n=1, 20000, write("b013680.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Apr 29 2009
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A013681
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Continued fraction for zeta(5).
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+10
5
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1, 27, 12, 1, 1, 15, 1, 5, 1, 2, 19, 1, 1, 32, 1, 13, 1, 1, 1, 3, 1, 3, 2, 16, 1, 12, 4, 1, 5, 1, 1, 1, 1, 1, 2, 2, 6, 1, 8, 8, 6, 2, 3, 2, 2, 1, 30, 1, 17, 116, 1, 7, 1, 1, 1, 1, 1, 1, 2, 2, 12, 1, 4, 1, 1, 94, 1, 1, 3, 3, 6, 6, 1, 1, 2, 1, 17, 1, 1, 7, 1, 1, 11
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A013682
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Continued fraction for zeta(6).
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+10
2
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1, 57, 1, 1, 1, 15, 1, 6, 3, 61, 1, 5, 3, 1, 6, 1, 3, 3, 6, 1, 10, 1, 3, 2, 1, 4, 1, 1, 5, 1, 61, 1, 3, 1, 2, 1, 3, 2, 1, 3, 1, 2, 2, 28, 1, 2, 18, 53, 2, 1, 17, 11, 3, 4, 3, 5, 2, 1, 27, 9, 8, 3, 3, 3, 9, 5, 1, 3, 29, 1, 4, 1, 2, 40, 4, 8, 1, 3, 1, 2, 2, 1, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A013683
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Continued fraction for zeta(7).
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+10
2
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1, 119, 1, 3, 2, 1, 2, 1, 39, 2, 3, 12, 3, 1, 1, 1, 2, 6, 5, 1, 5, 1, 2, 1, 23, 2, 1, 5, 34, 2, 1, 1, 3, 47, 2, 1, 8, 16, 1, 4, 1, 2, 1, 1, 1, 10, 72, 1, 1, 1, 1, 1, 2, 3, 13, 1, 2, 1, 5, 1, 27, 2, 9283, 1, 36, 1, 1, 1, 1, 3, 3, 23, 27, 5, 2, 4, 1, 3, 16, 1, 4
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A013684
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Continued fraction for zeta(8).
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+10
2
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1, 245, 3, 1, 8, 4, 2, 3, 2, 1, 1, 4, 1, 3, 12, 2, 2, 34, 1, 1, 1, 1, 4, 9, 1, 56, 3, 38, 1, 1, 6, 1, 1, 1, 1, 3, 2, 1, 1, 5, 9, 3, 1, 11, 2, 3, 1, 5, 2, 2, 1, 4, 1, 27, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 72, 17, 1, 36, 1, 5, 6, 1, 4, 10, 1, 4, 1, 4, 1, 1, 1, 8
(list;
graph;
refs;
listen;
history;
text;
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OFFSET
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0,2
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LINKS
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A013685
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Continued fraction for zeta(9).
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+10
2
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1, 497, 1, 10, 5, 1, 1, 8, 3, 2, 2, 1, 2, 1, 2, 5, 4, 2, 49, 1, 3, 3, 1, 1, 2, 1, 2, 30, 4, 1, 17, 3, 8, 2, 1, 2, 1, 1, 10, 6, 9, 2, 3, 1, 22, 1, 2, 1, 1, 2, 1, 1, 2, 18, 1, 1, 1, 9, 1, 2, 9, 1, 5, 2, 4, 1, 5, 1, 2, 2, 2, 6, 1, 8, 1, 5, 1, 4, 1483, 1, 3, 1, 2, 7
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A013695
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Continued fraction for zeta(19).
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+10
2
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1, 524050, 1, 1, 2, 3, 1, 1, 1, 1, 3, 1, 2, 5, 14, 1, 5, 1, 3, 1, 3, 1, 3, 2, 1, 1, 1, 4, 1, 9, 1, 2, 1, 6, 2, 1, 1, 1, 76, 85, 1, 8, 1, 1, 7, 12, 7, 2, 1, 2, 4, 1, 3, 1, 22, 1, 3, 6, 1, 1, 1, 1, 1, 4, 1, 11, 1, 3, 1, 2, 1, 6, 1, 9, 1, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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MATHEMATICA
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ContinuedFraction[Zeta[19], 100] (* Paolo Xausa, Jul 03 2024 *)
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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A013686
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Continued fraction for zeta(10).
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+10
1
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1, 1005, 2, 4, 1, 98, 7, 11, 2, 1, 1, 6, 2, 3, 28, 1, 37, 1, 2, 7, 9, 13, 85, 4, 3, 34, 5, 3, 7, 4, 7, 1, 3, 2, 1, 22, 1, 1, 1, 1, 3, 15, 1, 9, 12, 1, 3, 3, 3, 1, 3, 2, 1, 2, 1, 1, 2, 10, 8, 2, 2, 11, 54, 4, 5, 1, 2, 2, 1, 3, 2, 1, 19, 4, 5, 1, 2, 2, 7, 1, 200
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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LINKS
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MATHEMATICA
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ContinuedFraction[Zeta[10], 100] (* Paolo Xausa, Jul 03 2024 *)
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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