A110977 Sequence of denominators associated with the continued fraction based on the sequence d(n)= distance of n from closest prime ( A051699).

1, 1, 1, 1, 2, 1, 3, 1, 4, 9, 13, 9, 22, 9, 31, 71, 102, 71, 173, 71, 244, 559, 803, 559, 1362, 3283, 11211, 25705, 36916, 25705, 62621, 25705, 88326, 202357, 695397, 1593151, 2288548, 1593151, 3881699, 9356549, 13238248, 9356549, 22594797, 9356549

Offset: 0

Author

Giorgio Balzarotti and Paolo P. Lava, Sep 28 2005

Keywords

• frac
• nonn

Examples

			if n = 2, B(n) = B(2) = 1 because B(0) = 1, B(1) = 1 * B(0) = 1 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, A110976.

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.