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 1-4 of 4 results.

A266409 a(n) = (A003309(n+2)-1) / 2; numbers n such that 2n+1 is a Ludic number (in A003309).

Original entry on oeis.org

1, 2, 3, 5, 6, 8, 11, 12, 14, 18, 20, 21, 23, 26, 30, 33, 35, 38, 41, 44, 45, 48, 53, 57, 59, 60, 63, 65, 71, 74, 78, 80, 86, 87, 89, 90, 96, 104, 105, 110, 111, 113, 116, 117, 119, 123, 128, 132, 138, 141, 143, 150, 153, 156, 164, 165, 168, 170, 176, 179, 180, 188, 191, 194, 198, 203, 207, 209, 210, 215
Offset: 1

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Author

Antti Karttunen, Jan 28 2016

Keywords

Comments

Ludic numbers from A003309(2) = 3 onward, decremented by one, then halved.

Links

Crossrefs

Complement: A266410.
Cf. A003309, A192490.
Cf. A266350 (least monotonic left inverse).
Cf. permutations A266418, A266638.
Cf. also A005097.

Formula

a(n) = (A003309(n+2)-1) / 2.
Other identities. For all n >= 1:
A266350(a(n)) = n.

A266410 a(n) = (A266419(n) - 1) / 2; numbers n such that 2n+1 is a nonludic number (in A192607).

Original entry on oeis.org

4, 7, 9, 10, 13, 15, 16, 17, 19, 22, 24, 25, 27, 28, 29, 31, 32, 34, 36, 37, 39, 40, 42, 43, 46, 47, 49, 50, 51, 52, 54, 55, 56, 58, 61, 62, 64, 66, 67, 68, 69, 70, 72, 73, 75, 76, 77, 79, 81, 82, 83, 84, 85, 88, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 102, 103, 106, 107, 108, 109, 112, 114, 115, 118, 120, 121
Offset: 1

Views

Author

Antti Karttunen, Jan 28 2016

Keywords

Comments

Odd nonludic numbers (A266419) decremented by one, then halved.

Links

Crossrefs

Complement: A266409.
Cf. A192490, A192607, A266419.
Cf. permutations A266418, A266638.
Cf. also A047845.

Formula

a(n) = (A266419(n) - 1) / 2.

A266418 Permutation of natural numbers: a(1) = 1, a(2n) = A266410(a(n)), a(2n+1) = A266409(1+a(n)).

Original entry on oeis.org

1, 4, 2, 10, 6, 7, 3, 22, 20, 15, 11, 16, 12, 9, 5, 40, 53, 37, 45, 29, 33, 24, 21, 31, 35, 25, 23, 19, 18, 13, 8, 68, 111, 85, 156, 64, 104, 75, 123, 51, 74, 56, 87, 43, 59, 39, 48, 54, 80, 61, 90, 46, 60, 42, 57, 36, 44, 34, 41, 27, 26, 17, 14, 107, 210, 167, 387, 133, 276, 229, 573, 101, 198, 158, 351, 120
Offset: 1

Views

Author

Antti Karttunen, Jan 28 2016

Keywords

Comments

This sequence can be represented as a binary tree. Each left hand child is produced as A266410(n), and each right hand child as A266409(1+n), when the parent node contains n:
|
...................1...................
4 2
10......../ \........6 7......../ \........3
/ \ / \ / \ / \
/ \ / \ / \ / \
/ \ / \ / \ / \
22 20 15 11 16 12 9 5
40 53 37 45 29 33 24 21 31 35 25 23 19 18 13 8
etc.

Links

Crossrefs

Inverse: A266417.
Cf. A266409, A266410.
Similar or related permutations: A237126, A266638.

Formula

a(1) = 1, after which: a(2n) = A266410(a(n)), a(2n+1) = A266409(1+a(n)).
As a composition of related permutations:
a(n) = A266638(A237126(n)).

A266637 a(1) = 1; for n > 1, if A192490(2*n + 1) = 1 [when 2n+1 is a Ludic number] a(n) = A003309(1+a(A266350(n)-1)), otherwise a(n) = A192607(a(n-A266350(n))).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 11, 8, 9, 17, 13, 10, 37, 14, 12, 19, 23, 15, 25, 67, 16, 43, 27, 21, 29, 18, 52, 22, 181, 20, 30, 47, 34, 41, 24, 36, 77, 88, 26, 97, 59, 39, 53, 115, 32, 42, 407, 28, 70, 33, 224, 61, 31, 44, 64, 227, 49, 121, 89, 57, 35, 131, 51, 71, 101, 113, 38, 125, 79, 287, 55, 72, 91, 146, 46, 58, 1361
Offset: 1

Views

Author

Antti Karttunen, Jan 28 2016

Keywords

Links

Crossrefs

Inverse: A266638.
Cf. A003309, A192490, A192607, A266350.
Related or similar permutations: A237126, A266417.

Formula

a(1) = 1; for n > 1, if A192490(2*n + 1) = 1 [when 2n+1 is Ludic number] a(n) = A003309(1+a(A266350(n)-1)), otherwise a(n) = A192607(a(n-A266350(n))).
As a composition of related permutations:
a(n) = A237126(A266417(n)).
Showing 1-4 of 4 results.

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