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A098290
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Recurrence sequence based on positions of digits in decimal places of Zeta(3) (Apery's constant).
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13
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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
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FORMULA
| a(0)=0, p(i)=position of first occurrence of a(i) in decimal places of Zeta(3), a(i+1)=p(i).
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EXAMPLE
| Zeta(3) = 1.2020569031595942853997...
a(0)=0, a(1)=2 because 2nd decimal = 0, a(2)=1 because first digit = 2, etc
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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
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CROSSREFS
| Cf. A002117 for digits of Zeta(3). Other recurrence sequences: A097614 for Pi, A098266 for e, A098289 for ln(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: A071926 A133103 A054781 * A160110 A139393 A037916
Adjacent sequences: A098287 A098288 A098289 * A098291 A098292 A098293
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KEYWORD
| nonn,base
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AUTHOR
| Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 02 2004
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