A084452 -id:A084452 - cp's OEIS frontend

A084455 Permutation of Z, obtained by reflecting the juggling sequence A084452 from positive to negative numbers (with zero thrown at beat 0), folded to N with functions N2Z and Z2N.

1, 10, 2, 12, 4, 14, 6, 8, 9, 20, 3, 22, 5, 24, 7, 16, 17, 18, 19, 32, 11, 28, 13, 34, 15, 26, 27, 38, 23, 30, 31, 44, 21, 46, 25, 36, 37, 50, 29, 40, 41, 42, 43, 58, 33, 52, 35, 48, 49, 62, 39, 64, 47, 54, 55, 56, 57, 72, 45, 60, 61, 74, 51, 76, 53, 66, 67, 68, 69, 70, 71, 86

Offset: 1

Antti Karttunen, Jun 02 2003

nonn

This permutation consists of three infinite cycles + infinite number of fixed points.

Inverse: A084466. Cf. also A084454, A084461, A084491, A084495, A084499, A065166.

[seq(Z2N(A084455_Z2Z(N2Z(n))),n=1..45)];
N2Z := n -> ((-1)^n)*floor(n/2);
Z2N := z -> 2*abs(z)+`if`((z < 1),1,0);
A084455_Z2Z := z -> z+`if`((z > 0), A084452(z),`if`((z >= -3),2*(-z), A084452(A084454((-z)-3))));

A084453 a(n) = n + A084452(n) - 3.

Original entry on oeis.org

2, 3, 4, 1, 7, 8, 9, 5, 6, 13, 11, 14, 10, 16, 12, 19, 20, 15, 22, 17, 18, 26, 23, 21, 28, 29, 24, 25, 33, 27, 34, 35, 30, 31, 32, 40, 41, 42, 36, 37, 38, 39, 48, 45, 49, 43, 44, 52, 46, 47, 56, 54, 50, 51, 59, 53, 61, 55, 64, 57, 58, 67, 60, 69, 62, 63, 73, 65, 66, 74, 68, 76

Offset: 1

Antti Karttunen, Jun 02 2003

nonn

Inverse: A084454.

Cf. A084455, A084459, A084489, A084493, A084497.

A084451 Juggling states associated with the juggling sequence A084452.

Original entry on oeis.org

7, 11, 13, 14, 7, 19, 25, 28, 14, 7, 35, 21, 26, 13, 22, 11, 37, 50, 25, 44, 22, 11, 69, 38, 19, 41, 52, 26, 13, 70, 35, 49, 56, 28, 14, 7, 67, 97, 112, 56, 28, 14, 7, 131, 73, 100, 50, 25, 76, 38, 19, 137, 84, 42, 21, 74, 37, 82, 41, 148, 74, 37, 146, 73, 164, 82, 41, 276

Offset: 0

Antti Karttunen, Jun 02 2003

nonn

A. Karttunen, Scheme-program for computing this sequence
Eric Weisstein's World of Mathematics, Siteswap

Positions of sevens (ground states): A084449. Same sequence in binary: A084451.

a(0)=7, a(n) = (A084451(n-1) + 2^A084452(n) - 1)/2.

A084458 An infinite juggling sequence using three balls: a(n) is the least (lowest) throw needed to ensure that none of the juggling states A084457[n..n+A006519(n)-1] occurs in A084457[0..n-1].

Original entry on oeis.org

4, 4, 6, 0, 5, 8, 0, 0, 3, 7, 0, 7, 0, 9, 0, 0, 7, 0, 10, 0, 0, 0, 7, 12, 0, 0, 0, 0, 4, 10, 0, 0, 9, 0, 0, 11, 0, 0, 0, 9, 0, 13, 0, 0, 0, 0, 9, 0, 14, 0, 0, 0, 0, 0, 5, 12, 0, 0, 0, 11, 0, 0, 14, 0, 0, 0, 0, 11, 0, 0, 15, 0, 0, 0, 0, 0, 10, 0, 16, 0, 0, 0, 0, 0, 0, 5, 13, 0, 0, 0, 13, 0, 0, 0, 15, 0, 0, 0

Offset: 1

Antti Karttunen, Jun 02 2003

nonn

The condition is equivalent to that A000265(A084457(n)) does not occur in A084457[0..n-1].

Index entries for sequences related to juggling
A. Karttunen, Scheme-program for computing this sequence

Variant: A084452. Positions of zeros, minus one: A084463.

cp's OEIS Frontend

A084455 Permutation of Z, obtained by reflecting the juggling sequence A084452 from positive to negative numbers (with zero thrown at beat 0), folded to N with functions N2Z and Z2N.

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Maple

A084453 a(n) = n + A084452(n) - 3.

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A084451 Juggling states associated with the juggling sequence A084452.

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A084458 An infinite juggling sequence using three balls: a(n) is the least (lowest) throw needed to ensure that none of the juggling states A084457[n..n+A006519(n)-1] occurs in A084457[0..n-1].

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