id:A072115 - OEIS Search Results

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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, 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 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`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`
	PROGRAM	`(PARI) \p150 contfrac(abs(solve(X=-1, 0, zeta(X)-X)))`
	CROSSREFS	`Cf. A069857.` `Sequence in context: A073572 A073356 A093032 this_sequence A079948 A106689 A027082` `Adjacent sequences: A072112 A072113 A072114 this_sequence A072116 A072117 A072118`
	KEYWORD	`base,cofr,easy,nonn`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 19 2002`

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.

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