A060804 Continued fraction for 2*zeta(3).
2, 2, 2, 9, 3, 10, 1, 4, 18, 1, 3, 5, 3, 1, 3, 3, 1, 1, 5, 3, 8, 1, 2, 1, 62, 1, 1, 1, 3, 2, 2, 1, 1, 5, 3, 1, 8, 2, 2, 34, 7, 1, 1, 5, 1, 2, 3, 3, 14, 9, 214, 11, 8, 23, 1, 8, 2, 10, 2, 2, 2, 1, 1, 6, 1, 8, 2, 1, 9, 2, 1, 11, 1, 3, 3, 4, 1, 28, 6, 1, 28, 1, 15, 1, 1, 1, 2
Offset: 0
Examples
2.404113806319188570799476323... = 2 + 1/(2 + 1/(2 + 1/(9 + 1/(3 + ...)))). - _Harry J. Smith_, Jul 12 2009
Links
- Harry J. Smith, Table of n, a(n) for n = 0..19999
- Y. V. Nesterenko, Zeta(3) and recurrence relations.
- Y. V. Nesterenko, A few remarks on zeta(3), Mathematical Notes, 59 (No. 6, 1996), 625-636.
Programs
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Maple
Digits := 100: t1 := evalf(2*Zeta(3)); convert(t1,confrac);
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Mathematica
ContinuedFraction[2 Zeta[3],90] (* Harvey P. Dale, Apr 25 2025 *)
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PARI
{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(2*zeta(3)); for (n=1, 20000, write("b060804.txt", n-1, " ", x[n])); } \\ Harry J. Smith, Jul 12 2009
Extensions
Offset changed by Andrew Howroyd, Jul 10 2024