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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 1-10 of 56 results. Next

A279341 a(1) = 0, a(2) = 1, for n > 2, if A079559(n) = 0, a(n) = 2*a(A256992(n)), otherwise a(n) = 1 + 2*a(A256992(n)).

Original entry on oeis.org

0, 1, 3, 7, 2, 6, 15, 5, 14, 13, 31, 4, 12, 30, 11, 29, 10, 27, 63, 28, 26, 9, 25, 62, 61, 23, 8, 24, 60, 22, 59, 21, 58, 55, 127, 20, 54, 57, 53, 126, 19, 51, 56, 52, 18, 125, 123, 50, 47, 17, 124, 122, 49, 121, 46, 45, 119, 16, 48, 120, 44, 118, 43, 117, 42, 111, 255, 116, 110, 41, 109, 254, 115, 107, 40, 108, 114, 253, 39, 106, 103
Offset: 1

Views

Author

Antti Karttunen, Dec 10 2016

Keywords

Comments

Note the indexing: the domain starts from 1, while the range includes also zero.

Links

Crossrefs

Inverse: A279342.
Cf. A000120, A070939, A079559, A256992, A256993, A279345.
Related or similar permutations: A054429, A243071, A279338, A279343, A279347.

Programs

Formula

a(1) = 0, a(2) = 1, for n > 2, if A079559(n) = 0 [when n is a term of A055938], a(n) = 2*a(A256992(n)), otherwise a(n) = 1 + 2*a(A256992(n)).
As a composition of other permutations:
a(n) = A054429(A279343(n)).
a(n) = A279343(A279347(n)).
a(n) = A243071(A279338(n)).
Other identities. For all n >= 1:
A000120(a(n)) = A279345(n).
For all n >= 2, A070939(a(n)) = A256993(n).

A279343 a(1) = 0, and for n > 1, if A079559(n) = 0, a(n) = 1 + 2*a(A256992(n)), otherwise a(n) = 2*a(A256992(n)).

Original entry on oeis.org

0, 1, 2, 4, 3, 5, 8, 6, 9, 10, 16, 7, 11, 17, 12, 18, 13, 20, 32, 19, 21, 14, 22, 33, 34, 24, 15, 23, 35, 25, 36, 26, 37, 40, 64, 27, 41, 38, 42, 65, 28, 44, 39, 43, 29, 66, 68, 45, 48, 30, 67, 69, 46, 70, 49, 50, 72, 31, 47, 71, 51, 73, 52, 74, 53, 80, 128, 75, 81, 54, 82, 129, 76, 84, 55, 83, 77, 130, 56, 85, 88, 78, 131, 57, 86
Offset: 1

Views

Author

Antti Karttunen, Dec 10 2016

Keywords

Comments

Note the indexing: the domain starts from 1, while the range includes also zero.

Links

Crossrefs

Inverse: A279344.
Cf. A000120, A070939, A079559, A256992, A256993, A279346.
Related or similar permutations: A054429, A156552, A279338, A279341, A279347.

Programs

Formula

a(1) = 0, and for n > 1, if A079559(n) = 0 [when n is a term of A055938], a(n) = 1 + 2*a(A256992(n)), otherwise a(n) = 2*a(A256992(n)).
As a composition of other permutations:
a(n) = A054429(A279341(n)).
a(n) = A279341(A279347(n)).
a(n) = A156552(A279338(n)).
Other identities. For all n >= 1:
A000120(a(n)) = A279346(n).
For all n >= 2, A070939(a(n)) = A256993(n).

A256991 If A079559(n) = 1, a(n) = A213714(n) - 1, otherwise a(n) = A234017(n).

Original entry on oeis.org

0, 1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 5, 6, 7, 7, 8, 8, 9, 10, 9, 10, 11, 12, 11, 13, 14, 12, 13, 14, 15, 15, 16, 16, 17, 18, 17, 18, 19, 20, 19, 21, 22, 20, 21, 22, 23, 24, 23, 25, 26, 24, 25, 27, 28, 26, 29, 30, 27, 28, 29, 30, 31, 31, 32, 32, 33, 34, 33, 34, 35, 36, 35, 37, 38, 36, 37, 38, 39, 40, 39, 41, 42, 40, 41, 43, 44, 42
Offset: 1

Views

Author

Antti Karttunen, Apr 15 2015

Keywords

Comments

In other words, if n = A005187(k) for some k >= 1, then a(n) = k-1, otherwise it must be that n = A055938(h) for some h, and then a(n) = h.
In binary trees like A233276 and A233278, a(n) gives the contents at the parent node of node containing n, for any n >= 1.
When iterating a(n), a(a(n)), a(a(a(n))), and so on, A070939(n) = A256478(n) + A256479(n) = A257248(n) + A257249(n) gives the number of steps needed to reach zero, from any starting value n >= 1.

Links

Crossrefs

Cf. A005187, A055938, A079559, A213714, A234017.
Cf. also A256992 (variant), A256478, A256479, A233276, A233278, A257248, A257249.

Programs

Formula

If A079559(n) = 1, a(n) = A213714(n) - 1, otherwise a(n) = A234017(n).
a(n) = A256992(n) - A079559(n) = A213714(n) + A234017(n) - A079559(n).

A279338 a(1) = 1, for n > 1, if A079559(n) = 0, a(n) = 2*a(A256992(n)), otherwise a(n) = A003961(a(A256992(n))).

Original entry on oeis.org

1, 2, 3, 5, 4, 6, 7, 9, 10, 15, 11, 8, 12, 14, 25, 21, 18, 35, 13, 20, 30, 27, 45, 22, 33, 49, 16, 24, 28, 50, 55, 75, 42, 77, 17, 36, 70, 63, 105, 26, 125, 175, 40, 60, 54, 39, 65, 90, 121, 81, 44, 66, 135, 99, 98, 147, 91, 32, 48, 56, 100, 110, 245, 165, 150, 143, 19, 84, 154, 225, 231, 34, 275, 385, 72, 140, 126, 51, 343, 210, 539, 189, 52
Offset: 1

Views

Author

Antti Karttunen, Dec 10 2016

Keywords

Comments

A more recursed variant of A279336.

Links

Crossrefs

Inverse: A279339.
Cf. A003961, A055938, A079559, A256992, A278502.
Related or similar permutations: A005940, A163511, A250246, A279336, A279341, A279343, A279348.

Programs

Formula

a(1) = 1; for n > 1, if A079559(n) = 0 [when n is a term of A055938], a(n) = 2*a(A256992(n)), otherwise a(n) = A003961(a(A256992(n))).
As a composition of other permutations:
a(n) = A163511(A279341(n)).
a(n) = A005940(1+A279343(n)).
a(n) = A250246(A279348(n)).

A256478 a(0) = 0; and for n >= 1, if A079559(n) = 1, then a(n) = 1 + a(A213714(n)-1), otherwise a(n) = a(A234017(n)).

Original entry on oeis.org

0, 1, 1, 2, 2, 1, 2, 3, 3, 2, 2, 3, 1, 2, 3, 4, 4, 3, 3, 3, 2, 2, 4, 2, 3, 3, 4, 1, 2, 3, 4, 5, 5, 4, 4, 4, 3, 3, 4, 3, 3, 3, 5, 2, 2, 4, 3, 4, 2, 4, 5, 3, 3, 2, 3, 4, 4, 5, 1, 2, 3, 4, 5, 6, 6, 5, 5, 5, 4, 4, 5, 4, 4, 4, 5, 3, 3, 4, 4, 4, 3, 4, 6, 3, 3, 3, 3, 5, 5, 4, 2, 2, 4, 3, 5, 3, 4, 5, 6, 2, 4, 4, 4, 5, 3, 4, 3, 3, 2, 5, 5, 3, 6, 2, 4, 4, 3, 4, 5, 5, 6, 1, 2, 3, 4, 5, 6, 7, 7
Offset: 0

Views

Author

Antti Karttunen, Apr 15 2015

Keywords

Comments

a(n) tells how many nonzero terms of A005187 are encountered when traversing toward the root of binary tree A233276, starting from the node containing n. This count includes both n (in case it is a term of A005187) and 1 (but not 0). See also comments in A256479 and A256991.
The 1's (seem to) occur at positions given by A000325.

Links

Crossrefs

One more than A257248.
Cf. A000120, A000325, A005187, A070939, A079559, A080791, A213714, A234017, A233275, A233276, A233277, A255559, A256479, A256991.

Formula

a(0) = 0; and for n >= 1, if A079559(n) = 1, then a(n) = 1 + a(A213714(n)-1), otherwise a(n) = a(A234017(n)).
a(n) = A000120(A233277(n)). [Binary weight of A233277(n).]
Other identities and observations. For all n >= 1:
a(n) = 1 + A257248(n) = 1 + A080791(A233275(n)).
a(n) = A070939(n) - A256479(n).
a(n) >= A255559(n).

A256479 a(1) = 0, and for n > 1, if A079559(n) = 0, then a(n) = 1 + a(A234017(n)), otherwise a(n) = a(A213714(n)-1).

Original entry on oeis.org

0, 1, 0, 1, 2, 1, 0, 1, 2, 2, 1, 3, 2, 1, 0, 1, 2, 2, 2, 3, 3, 1, 3, 2, 2, 1, 4, 3, 2, 1, 0, 1, 2, 2, 2, 3, 3, 2, 3, 3, 3, 1, 4, 4, 2, 3, 2, 4, 2, 1, 3, 3, 4, 3, 2, 2, 1, 5, 4, 3, 2, 1, 0, 1, 2, 2, 2, 3, 3, 2, 3, 3, 3, 2, 4, 4, 3, 3, 3, 4, 3, 1, 4, 4, 4, 4, 2, 2, 3, 5, 5, 3, 4, 2, 4, 3, 2, 1, 5, 3, 3, 3, 2, 4, 3, 4, 4, 5, 2, 2, 4, 1, 5, 3, 3, 4, 3, 2, 2, 1, 6, 5, 4, 3, 2, 1, 0, 1
Offset: 1

Views

Author

Antti Karttunen, Apr 15 2015

Keywords

Comments

a(n) tells how many terms of A055938 are encountered when traversing toward the root of binary tree A233276, starting from the node containing n. This count includes also n in case it itself is a term of A055938. See also comments in A256478 and A256991.

Links

Crossrefs

One less than A257249.
Cf. A000120, A055938, A070939, A079559, A080791, A213714, A234017, A233275, A233276, A233277, A256478, A256991.
Cf. also A000225 (gives the positions zeros).

Formula

a(1) = 0, and for n > 1, if A079559(n) = 0, then a(n) = 1 + a(A234017(n)), otherwise a(n) = a(A213714(n)-1).
a(n) = A080791(A233277(n)). [Number of nonleading zeros in the binary representation of A233277(n).]
Other identities. For all n >= 1:
a(n) = A257249(n) - 1 = A000120(A233275(n)) - 1.
a(n) = A070939(n) - A256478(n).
a(A000225(n)) = 0.

A257248 a(1) = 0; and for n > 1, if A079559(n) = 1, then a(n) = 1 + a(A213714(n)-1), otherwise a(n) = a(A234017(n)).

Original entry on oeis.org

0, 0, 1, 1, 0, 1, 2, 2, 1, 1, 2, 0, 1, 2, 3, 3, 2, 2, 2, 1, 1, 3, 1, 2, 2, 3, 0, 1, 2, 3, 4, 4, 3, 3, 3, 2, 2, 3, 2, 2, 2, 4, 1, 1, 3, 2, 3, 1, 3, 4, 2, 2, 1, 2, 3, 3, 4, 0, 1, 2, 3, 4, 5, 5, 4, 4, 4, 3, 3, 4, 3, 3, 3, 4, 2, 2, 3, 3, 3, 2, 3, 5, 2, 2, 2, 2, 4, 4, 3, 1, 1, 3, 2, 4, 2, 3, 4, 5, 1, 3, 3, 3, 4, 2, 3, 2, 2, 1, 4, 4, 2, 5, 1, 3, 3, 2, 3, 4, 4, 5, 0, 1, 2, 3, 4, 5, 6, 6
Offset: 1

Views

Author

Antti Karttunen, Apr 19 2015

Keywords

Comments

a(n) tells how many nonzero terms of A005187 are encountered when traversing toward the root of binary tree A233276, starting from the node containing n and before 1 is reached. This count includes both n (in case it is a term of A005187) but excludes the 1 and 0 at the root. See also comments in A257249, A256478 and A256991.

Links

Crossrefs

One less than A256478.
Cf. A000120, A000325, A005187, A070939, A079559, A080791, A213714, A234017, A233275, A233276, A233277, A255559, A257249, A256991.

Formula

a(1) = 0; and for n > 1, if A079559(n) = 1, then a(n) = 1 + a(A213714(n)-1), otherwise a(n) = a(A234017(n)).
a(n) = A080791(A233275(n)). [Number of nonleading zeros in the binary representation of A233275(n).]
Other identities. For all n >= 1:
a(n) = A256478(n)-1 = A000120(A233277(n))-1.
a(n) = A070939(n) - A257249(n).

A257249 a(0) = 1, and for n >= 1, if A079559(n) = 0, then a(n) = 1 + a(A234017(n)), otherwise a(n) = a(A213714(n)-1).

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 2, 1, 2, 3, 3, 2, 4, 3, 2, 1, 2, 3, 3, 3, 4, 4, 2, 4, 3, 3, 2, 5, 4, 3, 2, 1, 2, 3, 3, 3, 4, 4, 3, 4, 4, 4, 2, 5, 5, 3, 4, 3, 5, 3, 2, 4, 4, 5, 4, 3, 3, 2, 6, 5, 4, 3, 2, 1, 2, 3, 3, 3, 4, 4, 3, 4, 4, 4, 3, 5, 5, 4, 4, 4, 5, 4, 2, 5, 5, 5, 5, 3, 3, 4, 6, 6, 4, 5, 3, 5, 4, 3, 2, 6, 4, 4, 4, 3, 5, 4, 5, 5, 6, 3, 3, 5, 2, 6, 4, 4, 5, 4, 3, 3, 2, 7, 6, 5, 4, 3, 2, 1, 2
Offset: 0

Views

Author

Antti Karttunen, Apr 19 2015

Keywords

Comments

Because A233275(n) = A003188(n) for n = 1 .. 9, a(n) = A005811(n) for n = 1 .. 9.

Links

Crossrefs

One more than A256479.
Cf. A000120, A003188, A005811, A055938, A070939, A079559, A080791, A213714, A234017, A233275, A233277, A233278, A257248, A256991.

Formula

a(0) = 1, and for n >= 1, if A079559(n) = 0, then a(n) = 1 + a(A234017(n)), otherwise a(n) = a(A213714(n)-1).
Other identities. For all n >= 1:
a(n) = A070939(n) - A257248(n).
a(n) = A000120(A233275(n)). [Binary weight of A233275(n).]
a(n) = 1 + A256479(n) = 1 + A080791(A233277(n)).

A279336 Permutation of natural numbers: a(1) = 1; for n > 1, if A079559(n) = 0, a(n) = 2*A234016(n), otherwise a(n) = A003961(a(A213714(n))).

Original entry on oeis.org

1, 2, 3, 5, 4, 6, 7, 9, 8, 15, 11, 10, 12, 14, 25, 27, 16, 35, 13, 18, 20, 21, 45, 22, 33, 49, 24, 26, 28, 30, 125, 81, 32, 77, 17, 34, 36, 75, 63, 38, 55, 175, 40, 42, 44, 39, 65, 46, 121, 135, 48, 50, 51, 99, 52, 105, 343, 54, 56, 58, 60, 62, 625, 243, 64, 143, 19, 66, 68, 57, 225, 70, 245, 275, 72, 74, 76, 69, 91, 78, 539, 189, 80
Offset: 1

Views

Author

Antti Karttunen, Dec 10 2016

Keywords

Comments

For n > 1, a(n) = the number which is in the same position of array A246278 where n is located in array A256997.

Links

Crossrefs

Inverse permutation: A279337.
Cf. A003961, A005187, A079559, A213714, A234016, A246278, A256997, A256998.
Cf. also A278501, A279338 (a variant).

Programs

Formula

a(1) = 1, for n > 1, if A079559(n) = 0 [when n is a term of A055938], a(n) = 2*A234016(n), otherwise a(n) = A003961(a(A213714(n))).
Other identities:
For all n >= 2, a(n) = A246278(A256998(n)).

A279348 a(1) = 1, for n > 1, if A079559(n) = 0, a(n) = 2*a(A256992(n)), otherwise a(n) = A250469(a(A256992(n))).

Original entry on oeis.org

1, 2, 3, 5, 4, 6, 7, 9, 10, 15, 11, 8, 12, 14, 25, 27, 18, 35, 13, 20, 30, 21, 33, 22, 39, 49, 16, 24, 28, 50, 65, 51, 54, 77, 17, 36, 70, 57, 87, 26, 55, 85, 40, 60, 42, 63, 95, 66, 121, 45, 44, 78, 69, 81, 98, 147, 119, 32, 48, 56, 100, 130, 125, 159, 102, 143, 19, 108, 154, 105, 207, 34, 145, 215, 72, 140, 114, 75, 91, 174, 133, 117, 52
Offset: 1

Views

Author

Antti Karttunen, Dec 12 2016

Keywords

Links

Crossrefs

Inverse: A279349.
Cf. A005187, A055938, A079559, A250469, A256992.
Related or similar permutations: A250245, A252753, A252755, A279338, A279341, A279343.

Programs

Formula

a(1) = 1, for n > 1, if A079559(n) = 0 [when n is a term of A055938], a(n) = 2*a(A256992(n)), otherwise a(n) = A250469(a(A256992(n))).
As a composition of other permutations:
a(n) = A250245(A279338(n)).
a(n) = A252753(A279343(n)).
a(n) = A252755(A279341(n)).
Showing 1-10 of 56 results. Next

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