A134566 -id:A134566 - cp's OEIS frontend

A134570 Array T(n,k) by antidiagonals; T(n,k) = position in row n of k-th occurrence of the Fibonacci number F(2n+1) in A134566.

2, 5, 1, 7, 4, 3, 10, 6, 11, 8, 13, 9, 16, 29, 21, 15, 12, 24, 42, 76, 55, 18, 14, 32, 63, 110, 199, 144, 20, 17, 37, 84, 165, 288, 521, 377, 23, 19, 45, 97, 220, 432, 754

Offset: 1

Clark Kimberling, Nov 02 2007

(Row 1) = A001950, the upper Wythoff sequence (Row 2) = (Column 1 of Wythoff array) = A003622 (Row 3) = (Column 3 of Wythoff array) = A035337 (Row 4) = (Column 5 of Wythoff array) = A035339 Except for initial terms, the first two columns of A134570 are bisected Fibonacci and Lucas sequences, A001906 and A002878, resp. Row 1 is the ordered union of all even-numbered columns of the Wythoff array; and A134570 is a permutation of the positive integers.

			Northwest corner:
2 5 7 10 13 15 18 20 23 26
1 4 6 9 12 14
3 11 16 24 32 37
8 29 42 63 84 97
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.

Cf. A134566, A134571.

A134567 a(n) = least m such that {-mtau} < {ntau}, 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

Clark Kimberling, Nov 01 2007

nonn

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.

			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}.

Cf. A134566, A134570, A134571.

cp's OEIS Frontend

A134570 Array T(n,k) by antidiagonals; T(n,k) = position in row n of k-th occurrence of the Fibonacci number F(2n+1) in A134566.

Views

Author

Keywords

Comments

Examples

Crossrefs

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

Views

Author

Keywords

Comments

Examples

Crossrefs

cp's OEIS Frontend

A134570 Array T(n,k) by antidiagonals; T(n,k) = position in row n of k-th occurrence of the Fibonacci number F(2n+1) in A134566.

Views

Author

Keywords

Comments

Examples

Crossrefs

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

Views

Author

Keywords

Comments

Examples

Crossrefs

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