A110917 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).

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

Offset

1,1

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.

References

G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 110.

Links

Table of n, a(n) for n=1..105.

Formula

see program

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+...

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:

Crossrefs

Cf. A051699, A110976, A110977.

Sequence in context: A308117 A270755 A305030 * A329340 A070956 A237127

Adjacent sequences: A110914 A110915 A110916 * A110918 A110919 A110920

Keyword

cofr,nonn

Author

Giorgio Balzarotti and Paolo P. Lava, Oct 04 2005

Status

approved