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.

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

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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)).

A266638 a(1) = 1, a(ludic(n)) = (ludic(3+a(n-1))-1)/2, a(nonludic(n)) = A266410(a(n)), where ludic(n) = n-th ludic number A003309, nonludic(n) = n-th nonludic number A192607 and A266410 = numbers n such that 2n+1 is nonludic.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 9, 10, 13, 8, 16, 12, 15, 19, 22, 11, 27, 17, 31, 25, 29, 18, 36, 20, 40, 24, 49, 26, 32, 54, 46, 51, 34, 62, 37, 14, 68, 43, 81, 35, 47, 23, 55, 88, 76, 33, 83, 58, 99, 64, 28, 44, 107, 72, 127, 61, 77, 42, 91, 53, 136, 121, 56, 130, 94, 21, 151, 101, 50, 65, 73, 161, 114, 189, 98, 38
Offset: 1

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Author

Antti Karttunen, Jan 28 2016

Keywords

Links

Crossrefs

Inverse: A266637.
Cf. A003309, A192490, A192512, A236863, A266409, A266410.
Related or similar permutations: A237427, A266418.

Formula

a(1) = 1; for n > 1, if A192490(n) = 1 [when n is one of Ludic numbers, A003309] a(n) = A266409(1+a(A192512(n)-1)), otherwise a(n) = A266410(a(A236863(n))).
As a composition of related permutations:
a(n) = A266418(A237427(n)).

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.

A266419 Odd nonludic numbers.

Original entry on oeis.org

9, 15, 19, 21, 27, 31, 33, 35, 39, 45, 49, 51, 55, 57, 59, 63, 65, 69, 73, 75, 79, 81, 85, 87, 93, 95, 99, 101, 103, 105, 109, 111, 113, 117, 123, 125, 129, 133, 135, 137, 139, 141, 145, 147, 151, 153, 155, 159, 163, 165, 167, 169, 171, 177, 183, 185, 187, 189, 191, 195, 197, 199, 201, 203, 205, 207, 213, 215
Offset: 1

Views

Author

Antti Karttunen, Jan 28 2016

Keywords

Links

Crossrefs

Intersection of A005408 and A192607.
Cf. A192490, A266410, A237126.
Cf. also A071904, A266420.

Formula

Other identities. For all n >= 1:
a(n) = 1 + 2*A266410(n).
Showing 1-4 of 4 results.

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