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A110917
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Conversion to a regular-simple continued-fraction approximation of the limit value (C0=2.7745963816360040537087...) 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
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OFFSET
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1,1
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COMMENTS
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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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REFERENCES
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G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 110.
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LINKS
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FORMULA
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see program
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EXAMPLE
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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
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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
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KEYWORD
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cofr,nonn
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AUTHOR
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STATUS
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approved
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