A110976 Sequence of numerators associated with the continued fraction based on the sequence d(n)= distance of n from closest prime ( A051699).

2, 3, 2, 3, 5, 3, 8, 3, 11, 25, 36, 25, 61, 25, 86, 197, 283, 197, 480, 197, 677, 1551, 2228, 1551, 3779, 9109, 31106, 71321, 102427, 71321, 173748, 71321, 245069, 561459, 1929446, 4420351, 6349797, 4420351, 10770148, 25960647, 36730795, 25960647

Offset: 0

Author

Giorgio Balzarotti and Paolo P. Lava, Sep 28 2005

Keywords

• frac
• nonn

Comments

The value of the continued fraction (for n to infinity) is 2.77459638163600405370875399896...; A(n) = A(n+2) if d(n) =2 and d(n+2) = 0

Examples

			if n = 2, A(n) = A(2) = 3 because A(0) = 2, A(1) = 1 * A(0) + 1 = 3, as the distances of n from closest prime are 2, 1, 0, 0, 1 ...
		

References

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

Crossrefs

Cf. A051699, A109139, A109140, A110977.

Programs

Maple

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;

Formula

See program