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Search: a013631 -id:a013631
Displaying 11-20 of 30 results found.
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A013683
Continued fraction for zeta(7).
+10
2
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)
OFFSET
0,2
LINKS
T. D. Noe, Table of n, a(n) for n = 0..9999
Index entries for continued fractions for constants
Index entries for zeta function
MATHEMATICA
ContinuedFraction[Zeta[7], 100] (* Harvey P. Dale, Sep 13 2020 *)
CROSSREFS
Cf. A013665 (decimal expansion).
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.
KEYWORD
nonn,cofr
AUTHOR
N. J. A. Sloane
EXTENSIONS
Offset changed by Andrew Howroyd, Jul 09 2024
STATUS
approved
A013684
Continued fraction for zeta(8).
+10
2
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; internal format)
OFFSET
0,2
LINKS
T. D. Noe, Table of n, a(n) for n = 0..9999
Index entries for continued fractions for constants
Index entries for zeta function
MATHEMATICA
ContinuedFraction[Zeta[8], 80] (* Harvey P. Dale, Aug 14 2020 *)
CROSSREFS
Cf. A013666 (decimal expansion).
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.
KEYWORD
nonn,cofr
AUTHOR
N. J. A. Sloane
EXTENSIONS
Offset changed by Andrew Howroyd, Jul 09 2024
STATUS
approved
A013685
Continued fraction for zeta(9).
+10
2
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)
OFFSET
0,2
LINKS
T. D. Noe, Table of n, a(n) for n = 0..9999
Index entries for continued fractions for constants
Index entries for zeta function
MATHEMATICA
ContinuedFraction[Zeta[9], 100] (* Harvey P. Dale, Aug 05 2023 *)
CROSSREFS
Cf. A013667 (decimal expansion).
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.
KEYWORD
nonn,cofr
AUTHOR
N. J. A. Sloane
EXTENSIONS
Offset changed by Andrew Howroyd, Jul 09 2024
STATUS
approved
A013695
Continued fraction for zeta(19).
+10
2
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)
OFFSET
0,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..9999
Index entries for continued fractions for constants
Index entries for zeta function
MATHEMATICA
ContinuedFraction[Zeta[19], 100] (* Paolo Xausa, Jul 03 2024 *)
CROSSREFS
Cf. A013677 (decimal expansion).
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.
KEYWORD
nonn,cofr
AUTHOR
N. J. A. Sloane
EXTENSIONS
Offset changed by Andrew Howroyd, Aug 10 2024
STATUS
approved
A033166
Incrementally largest terms in the continued fraction for zeta(3).
+10
2
1, 4, 18, 30, 428, 458, 527, 542, 659, 922, 1355, 1817, 3292, 4635, 6841, 162050, 197106, 270086, 270919, 344064, 2079442, 5492021, 196362299, 220581908, 1292221854, 5841289122, 11886461834
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..27.
Eric Weisstein's World of Mathematics, Apery's Constant Continued Fraction
CROSSREFS
Cf. A013631 (continued fraction of zeta(3)).
Cf. A229055 (positions of incrementally largest terms in the c.f. of zeta(3)).
Cf. A033165, A000023, A229055.
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane
EXTENSIONS
More terms from Eric W. Weisstein, Aug 23 2000
More terms from Robert Gerbicz, Aug 22 2006
More terms from Eric W. Weisstein, Sep 16 2013
a(27) = 11886461834 from Eric W. Weisstein, Sep 17 2013
STATUS
approved
A078985
Denominators of continued fraction convergents to zeta(3).
+10
2
1, 4, 5, 94, 99, 193, 292, 1361, 1653, 16238, 147795, 311828, 459623, 771451, 1231074, 3233599, 23866267, 27099866, 50966133, 383862797, 4273456900, 4657319697, 8930776597, 13588096294, 49695065479, 63283161773, 429394036117
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Table of n, a(n) for n=0..26.
PROG
(PARI) a(n)=component(component(contfracpnqn(contfrac(zeta(3), n+1)), 1), 2)
CROSSREFS
Cf. A078984 (numerators), A013631 (continued fraction).
KEYWORD
cofr,frac,nonn
AUTHOR
Benoit Cloitre, Dec 20 2002
EXTENSIONS
Offset changed by Andrew Howroyd, Jul 10 2024
STATUS
approved
A229055
Positions of the incrementally largest terms in the continued fraction expansion of zeta(3).
+10
2
0, 1, 3, 28, 62, 571, 1555, 2012, 2529, 2759, 3018, 4158, 4740, 6819, 10564, 11665, 32858, 139892, 392129, 707969, 1049721, 2081164, 14990403, 36112275, 39552834, 42710786, 199618805
(list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
A033167 has the same information but indexed differently. - N. J. A. Sloane, Jun 16 2021
LINKS
Table of n, a(n) for n=1..27.
Eric Weisstein's World of Mathematics, Apery's Constant Continued Fraction
FORMULA
A033166(n) = A013631(a(n)). - Andrew Howroyd, Jul 10 2024
CROSSREFS
Cf. A033166, A033167 (= a(n) + 1), A013631 (continued fraction for zeta(3)).
KEYWORD
nonn,more
AUTHOR
Eric W. Weisstein, Sep 16 2013
EXTENSIONS
a(27) = 199618805 from Eric W. Weisstein, Sep 17 2013
STATUS
approved
A013686
Continued fraction for zeta(10).
+10
1
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)
OFFSET
0,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..9999
Index entries for continued fractions for constants
Index entries for zeta function
MATHEMATICA
ContinuedFraction[Zeta[10], 100] (* Paolo Xausa, Jul 03 2024 *)
CROSSREFS
Cf. A013668 (decimal expansion).
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.
KEYWORD
nonn,cofr
AUTHOR
N. J. A. Sloane
EXTENSIONS
Offset changed by Andrew Howroyd, Jul 09 2024
STATUS
approved
A013688
Continued fraction for zeta(12).
+10
1
1, 4063, 1, 1, 1, 1, 3, 14, 4, 5, 1, 8, 3, 1, 142, 1, 2, 1, 2, 2, 24, 1, 3, 20, 1, 1, 1, 60, 4, 1, 12, 1, 1, 1, 4, 23, 12, 1, 3, 11, 1, 2, 1, 13, 3, 16, 1, 91, 2, 2, 8, 1, 1, 1, 62, 1, 7, 1, 2, 15, 2, 5, 4, 1, 8, 1, 1, 20, 2, 2, 1, 1, 3, 2, 1, 1, 1, 1, 2, 1, 1
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..9999
Index entries for continued fractions for constants
Index entries for zeta function
MATHEMATICA
ContinuedFraction[Zeta[12], 100] (* Paolo Xausa, Jul 03 2024 *)
CROSSREFS
Cf. A013670 (decimal expansion).
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.
KEYWORD
nonn,cofr
AUTHOR
N. J. A. Sloane
EXTENSIONS
Offset changed by Andrew Howroyd, Jul 09 2024
STATUS
approved
A013694
Continued fraction for zeta(18).
+10
1
1, 261965, 1, 2, 1, 1, 1, 4, 3, 4, 3, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 4, 1, 3, 3, 1, 2, 5, 1, 2, 3, 6, 1, 8, 3, 9, 1, 1, 1, 2, 3, 1, 1, 2, 1, 3, 1, 1, 1, 9, 1, 1, 21, 1, 3, 1, 3, 3, 3, 1, 1, 6, 4, 3, 5, 2, 1, 1, 26, 21, 6, 1, 11, 24, 1
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
Paolo Xausa, Table of n, a(n) for n = 0..9999
Index entries for continued fractions for constants
Index entries for zeta function
MATHEMATICA
ContinuedFraction[Zeta[18], 100] (* Paolo Xausa, Jul 03 2024 *)
CROSSREFS
Cf. A013676 (decimal expansion).
Cf. continued fractions for zeta(2)-zeta(20): A013679, A013631, A013680-A013696.
KEYWORD
nonn,cofr
AUTHOR
N. J. A. Sloane
EXTENSIONS
Offset changed by Andrew Howroyd, Aug 10 2024
STATUS
approved
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