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.

A134571 Array T(n,k) by antidiagonals; T(n,k) = position in row n of k-th occurrence of the Fibonacci number F(2n) in A134567.

Original entry on oeis.org

1, 3, 2, 4, 7, 5, 6, 10, 18, 13, 8, 15, 26, 47, 34, 9, 20, 39, 68, 123, 89, 11, 23, 52, 102, 178, 322, 233
Offset: 1

Views

Author

Clark Kimberling, Nov 02 2007

Keywords

Comments

(Row 1) = A000201, the lower Wythoff sequence (Row 2) = (Column 2 of Wythoff array) = A035336 (Row 3) = (Column 4 of Wythoff array) = A035338 (Row 4) = (Column 6 of Wythoff array) = A035340 (Column 1) = A001519 (bisection of Fibonacci sequence) (Column 2) = A005248 (bisection of Lucas sequence) (Column 3) = A052995 Row 1 is the ordered union of all odd-numbered columns of the Wythoff array; and A134571 is a permutation of the positive integers.
It looks like this array is A080164 transposed. - Peter Munn, Sep 02 2025

Examples

			Northwest corner:
1 3 4 6 8 9 11 12 14 16
2 7 10 15 20 23
5 18 26 39 52 60
13 47 68 102 136 157
Row 1 consists of numbers k such that 1 is the least m for which {-m*tau}<{k*tau}, where tau=(1+sqrt(5))/2 and {} denotes fractional part.

Crossrefs

Cf. A080164, A134567, A134570.

A134566 a(n) = least m such that {-m*tau} > {n*tau}, where { } denotes fractional part and tau = (1 + sqrt(5))/2.

Original entry on oeis.org

2, 1, 5, 2, 1, 2, 1, 13, 2, 1, 5, 2, 1, 2, 1, 5, 2, 1, 2, 1, 34, 2, 1, 5, 2, 1, 2, 1, 13, 2, 1, 5, 2, 1, 2, 1, 5, 2, 1, 2, 1, 13, 2, 1, 5, 2, 1, 2, 1, 5, 2, 1, 2, 1, 89, 2, 1, 5, 2, 1, 2, 1, 13, 2, 1, 5, 2, 1, 2, 1, 5, 2, 1, 2, 1, 34, 2, 1, 5, 2, 1, 2, 1, 13, 2, 1, 5, 2, 1, 2, 1, 5, 2, 1, 2, 1, 13, 2, 1, 5, 2, 1
Offset: 1

Views

Author

Clark Kimberling, Nov 01 2007, Nov 02 2007

Keywords

Comments

The terms are members of A001519, the odd-indexed Fibonacci numbers. The defining inequality {-m*tau} > {n*tau} is equivalent to {-m*tau} + {n*tau} < 1.
The terms belong to A001519, the odd-indexed Fibonacci numbers. The defining inequality {-m*tau} > {n*tau} is equivalent to {m*tau} + {n*tau} < 1. - Clark Kimberling, Nov 02 2007

Examples

			a(3)=5 because {m*tau} < {3*tau} = 0.854... for m=1,2,3,4, whereas {-5*tau} = 0.909..., so that 5 is the least m for which {m*tau} > {3*tau}.
a(3)=5 because {-m*tau} < {3*tau} = 0.854... for m=1,2,3,4 whereas {-5*tau} = 0.9289..., so that 5 is the least m for which {-m*tau} > {2*tau}.

Crossrefs

Cf. A134567, A134570, A134571.

Extensions

More terms from Clark Kimberling, Nov 02 2007

A134567 a(n) = least m such that {-m*tau} < {n*tau}, where { } denotes fractional part and tau = (1 + sqrt(5))/2.

Original entry on oeis.org

1, 3, 1, 1, 8, 1, 3, 1, 1, 3, 1, 1, 21, 1, 3, 1, 1, 8, 1, 3, 1, 1, 3, 1, 1, 8, 1, 3, 1, 1, 3, 1, 1, 55, 1, 3, 1, 1, 8, 1, 3, 1, 1, 3, 1, 1, 21, 1, 3, 1, 1, 8, 1, 3, 1, 1, 3, 1, 1, 8, 1, 3, 1, 1, 3, 1, 1, 21, 1, 3, 1, 1, 8, 1, 3, 1, 1, 3, 1, 1, 8, 1, 3, 1, 1, 3, 1, 1, 144, 1, 3, 1, 1, 8, 1, 3, 1, 1, 3, 1, 1, 21
Offset: 1

Views

Author

Clark Kimberling, Nov 01 2007

Keywords

Comments

The terms are members of A001906, the even-indexed Fibonacci numbers. The defining inequality {-m*tau} < {n*tau} is equivalent to {m*tau} + {n*tau} > 1.

Examples

			a(2)=3 because {-m*tau} > {2*tau} = 0.236... for m=1,2, whereas {-3*tau} = 0.145..., so that 3 is the least m for which {-m*tau} < {3*tau}.

Crossrefs

Cf. A134566, A134570, A134571.
Showing 1-3 of 3 results.

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