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A098290 Recurrence sequence based on positions of digits in decimal places of Zeta(3) (Apery's constant). 13


%S 0,2,1,10,208,380,394,159,10,208,380,394,159,10,208,380,394,159,10,

%T 208,380,394,159,10,208,380,394,159,10,208,380,394,159,10,208,380,394,

%U 159,10,208,380,394,159,10,208,380,394,159,10,208,380,394,159,10

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

%C This recurrence sequence starts to repeat quite quickly because 1 appears at the 10th digit of Zeta(3), which is also where 159 starts.

%C Can the transcendental numbers such that recurrence relations of this kind eventually repeat be characterized? - _Nathaniel Johnston_, Apr 30 2011

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

%e Zeta(3) = 1.2020569031595942853997...

%e a(0)=0, a(1)=2 because 2nd decimal = 0, a(2)=1 because first digit = 2, etc.

%p 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

%Y 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).

%K nonn,base

%O 0,2

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

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Last modified December 16 09:06 EST 2019. Contains 330020 sequences. (Running on oeis4.)