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
Examples
Zeta(3) = 1.2020569031595942853997... a(0)=0, a(1)=2 because 2nd decimal = 0, a(2)=1 because first digit = 2, etc.
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).
Programs
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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
Formula
a(0)=0, p(i)=position of first occurrence of a(i) in decimal places of Zeta(3), a(i+1)=p(i).
Comments