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A072115
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Continued fraction expansion of abs(C) where C=-0.2959050055752...is the real negative solution to zeta(x)=x.
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0
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0, 3, 2, 1, 1, 1, 2, 1, 7, 14, 1, 2, 10, 1, 5, 3, 1, 7, 2, 1, 2, 2, 2, 4, 1, 1, 12, 1, 1, 1, 14, 2, 10, 3, 5, 6, 2, 1, 6, 13, 1, 2, 2, 4, 8, 1, 4, 8, 2, 1, 16, 1, 1, 1, 1, 4, 2, 1, 1, 1, 3, 13, 4, 1, 2, 1, 6, 1, 1, 2, 43, 1, 3, 1, 1, 2, 2, 2, 1, 2, 2, 2, 10, 5, 4, 8, 1, 5, 3, 2, 1, 1, 3, 2, 19
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OFFSET
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1,2
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COMMENTS
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Start from any complex number z=x+iy, not solution to zeta(z)=z, iterate the zeta function on z. If zeta_m(z) (=zeta(zeta(....(z)..)) m times) has a limit when m grows, then this limit seems to always be the real number : C=-0.2959050055752....Example: if z=3+5I after 30 iterations : zeta_30(z)=-0.29590556499...-0.00000041029065...*I
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LINKS
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Table of n, a(n) for n=1..95.
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PROG
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(PARI) \p150 contfrac(abs(solve(X=-1, 0, zeta(X)-X)))
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CROSSREFS
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Cf. A069857.
Sequence in context: A073572 A073356 A093032 * A210650 A218754 A079948
Adjacent sequences: A072112 A072113 A072114 * A072116 A072117 A072118
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KEYWORD
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base,cofr,easy,nonn
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AUTHOR
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Benoit Cloitre, Jun 19 2002
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STATUS
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approved
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