cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A109140 Denominators associated with A109139.

Original entry on oeis.org

1, 1, 3, 7, 31, 69, 307, 683, 3039, 18917, 40873, 264155, 1097493, 2459141, 10934057, 68063483, 419314955, 906693393, 5859475313, 24344594645, 54548664603, 351636582263, 1461094993655, 9118206544193
Offset: 0

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Author

Giorgio Balzarotti, Aug 18 2005

Keywords

Crossrefs

Cf. A109139.

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

Original entry on oeis.org

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

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Author

Keywords

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

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

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

Original entry on oeis.org

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

Views

Author

Keywords

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

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.
Showing 1-3 of 3 results.