A013682 -id:A013682

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A343244

Position of the first occurrence of an element in the continued fraction of zeta(n) which is larger than the second element.

+10
0

5, 4, 8, 14, 10, 63, 120, 79, 1270, 779, 1749, 3410, 13668, 17704, 20909, 175782, 127426

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OFFSET

2,1

COMMENTS

a(20) = 111604.

The corresponding values of the a(n)-th elements are 4, 18, 183, 32, 61, 9283, 462, 1483, 3530, 3484, 10812, 8954, ...

LINKS

Table of n, a(n) for n=2..18.

EXAMPLE

The continued fraction of zeta(3) is [1; 4, 1, 18, 1, 1, ...]. The first element which is larger than 4 is 18 whose position is 4. Therefore, a(3) = 4.

MATHEMATICA

a[n_] := Module[{c = ContinuedFraction[Zeta[n], 10000]}, FirstPosition[c, _?(# > c[[2]] &)][[1]]]; Array[a, 10, 2]

CROSSREFS

Cf. A013697.

Cf. A013679, A013631, A013680, A013681, A013682, A013683, A013684, A013685.

KEYWORD

nonn,more

AUTHOR

Amiram Eldar, Apr 08 2021

STATUS

approved

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