A098290 Recurrence sequence based on positions of digits in decimal places of Zeta(3) (Apery's constant).

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

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[n-1], string), G)-1:printf("%d, ", a[n-1]):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: A370068 A239070 A271042 * A160110 A258055 A339306

Adjacent sequences: A098287 A098288 A098289 * A098291 A098292 A098293

Keyword

nonn,base

Author

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

Status

approved