

A098290


Recurrence sequence based on positions of digits in decimal places of Zeta(3) (Apery's constant).


13



0, 2, 1, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10, 208, 380, 394, 159, 10
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OFFSET

0,2


COMMENTS

This recurrence sequence starts to repeat quite quickly because 1 appears at the 10th digit of Zeta(3), which is also where 159 starts.
Can the transcendental numbers such that recurrence relations of this kind eventually repeat be characterized?  Nathaniel Johnston, Apr 30 2011


LINKS

Table of n, a(n) for n=0..53.


FORMULA

a(0)=0, p(i)=position of first occurrence of a(i) in decimal places of Zeta(3), a(i+1)=p(i).


EXAMPLE

Zeta(3) = 1.2020569031595942853997...
a(0)=0, a(1)=2 because 2nd decimal = 0, a(2)=1 because first digit = 2, etc.


MAPLE

with(StringTools): Digits:=400: G:=convert(evalf(Zeta(3)1), string): a[0]:=0: for n from 1 to 50 do a[n]:=Search(convert(a[n1], string), G)1:printf("%d, ", a[n1]):od: # Nathaniel Johnston, Apr 30 2011


CROSSREFS

Cf. A002117 for digits of Zeta(3). Other recurrence sequences: A097614 for Pi, A098266 for e, A098289 for log(2), A098290 for Zeta(3), A098319 for 1/Pi, A098320 for 1/e, A098321 for gamma, A098322 for G, A098323 for 1/G, A098324 for Golden Ratio (phi), A098325 for sqrt(Pi), A098326 for sqrt(2), A120482 for sqrt(3), A189893 for sqrt(5), A098327 for sqrt(e), A098328 for 2^(1/3).
Sequence in context: A213421 A239070 A271042 * A160110 A258055 A139393
Adjacent sequences: A098287 A098288 A098289 * A098291 A098292 A098293


KEYWORD

nonn,base


AUTHOR

Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 02 2004


STATUS

approved



