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.

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).

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).

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)).
Showing 1-3 of 3 results.

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