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A110917
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Conversion to a regular-simple continued-fraction approximation of the limit value (C0=2.774596381636004053708753998963780211275369098508432957319128835754771409356068438727613439124577996...) of the continued fraction (numerator = A110976 and denominator = A110977) based on the sequence of the distances of n from closest primes (A051699).
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0
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2, 1, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 4, 3, 2, 2, 2, 3, 2, 3, 2, 2, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 4, 5, 4, 3, 2, 3, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 4, 5
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| With the exception of n = 3, it should be abs(a(n)-a(n-1)) = < 1 for all n. Hill-mountain-like plot, with land = 2.
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FORMULA
| see program
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EXAMPLE
| C0 = a(1) +1/( a(2) +1/( a(3) +1/( a(4) +1/( a(5) +...=2+1/(1+1/(3+1/(2+1/(3+...
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MAPLE
| cd:=proc(N) # d[n]distance of n from closest prime A[0]:=d[0]; A[1]:=d[1]*A[0]+1; B[0]:=1; B[1]:=d[1]*B[0]; for n from 2 by 1 to N do A[n]:=d[n]*A[n-1]+A[n-2]; B[n]:=d[n]*B[n-1]+B[n-2]; od; R:=A[N]/B[N]; convert(R, confrac); end:
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CROSSREFS
| Cf. A051699, A110976, A110977.
Sequence in context: A026730 A075256 A001480 * A070956 A007828 A070804
Adjacent sequences: A110914 A110915 A110916 * A110918 A110919 A110920
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KEYWORD
| cofr,nonn
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AUTHOR
| Giorgio Balzarotti and Paolo P. Lava (greenblue(AT)tiscali.it), Oct 04 2005
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