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.

A245606 Permutation of natural numbers: a(1) = 1, a(2n) = 1 + A003961(a(n)), a(2n+1) = A003961(1+a(n)). [Where A003961(n) shifts the prime factorization of n one step left].

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 9, 10, 7, 8, 15, 16, 11, 26, 21, 22, 13, 12, 27, 28, 25, 36, 81, 82, 19, 14, 45, 52, 125, 56, 39, 40, 29, 18, 33, 46, 17, 126, 99, 100, 31, 50, 51, 226, 41, 626, 129, 130, 89, 24, 63, 34, 35, 176, 87, 154, 59, 344, 825, 298, 115, 86, 189, 190, 43, 32, 105, 76, 23, 66, 57, 88, 53, 20
Offset: 1

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Author

Antti Karttunen, Jul 29 2014

Keywords

Comments

The even bisection halved gives A245608. The odd bisection incremented by one and halved gives A245708.

Links

Crossrefs

Inverse: A245605.
Cf. A003961, A243501, A064216, A245608, A245706, A245708.
Similar entanglement permutations: A244319, A156552, A243071, A243288, A243344, A243346, A244322, A245604, A245614, A227413, A237126.

Programs

Formula

a(1) = 1, a(2n) = A243501(a(n)), a(2n+1) = A003961(1+a(n)).
As a composition of related permutations:
a(n) = A064216(A245608(n)).

A244152 Self-inverse permutation of natural numbers: a(1) = 1; thereafter, if n is k-th number with an odd number of prime divisors (counted with multiplicity) [i.e., n = A026424(k)], a(n) = A028260(1+a(k)), otherwise, when n is k-th number > 1 with an even number of prime divisors [i.e., n = A028260(1+k)], a(n) = A026424(a(k)).

Original entry on oeis.org

1, 4, 10, 2, 24, 7, 6, 55, 18, 3, 16, 15, 121, 44, 12, 11, 39, 9, 36, 35, 105, 31, 250, 5, 29, 28, 93, 26, 25, 86, 22, 82, 238, 79, 20, 19, 81, 72, 17, 68, 218, 65, 517, 14, 62, 67, 60, 202, 195, 57, 59, 56, 185, 477, 8, 52, 50, 175, 51, 47, 177, 45, 495, 167, 42, 161, 46, 40, 162, 169, 150, 38, 143, 455, 459, 140, 153, 1060, 34, 134, 37, 32
Offset: 1

Views

Author

Antti Karttunen, Jul 27 2014

Keywords

Links

Crossrefs

Cf. A008836, A026424, A028260, A055037, A055038, A066829.
Similar entanglement permutations: A245603-A245604, A235491, A236854, A243347, A244319.

Formula

a(1) = 1, and for n > 1, if A066829(n) = 1, then a(n) = A028260(1 + A244152(A055038(n))), otherwise a(n) = A026424(A244152(A055037(n)-1)).
For all n > 1, A008836(a(n)) = -1 * A008836(n), where A008836 is Liouville's lambda-function.

A245603 Permutation of natural numbers: a(1) = 1; thereafter, if n is k-th number with an odd number of prime divisors (counted with multiplicity) [i.e., n = A026424(k)], a(n) = 2*a(k), otherwise, when n is k-th number > 1 with an even number of prime divisors [i.e., n = A028260(1+k)], a(n) = 1+(2*a(k)).

Original entry on oeis.org

1, 2, 4, 3, 8, 5, 6, 16, 9, 7, 10, 12, 32, 17, 11, 13, 18, 14, 20, 24, 33, 19, 64, 15, 21, 25, 34, 22, 26, 36, 28, 40, 65, 35, 23, 27, 48, 37, 29, 41, 66, 38, 128, 30, 42, 49, 50, 68, 67, 44, 39, 52, 72, 129, 31, 43, 51, 69, 56, 45, 80, 53, 130, 73, 57, 70, 46, 54, 81, 96, 74, 58, 82, 131, 132, 76, 71, 256, 60
Offset: 1

Views

Author

Antti Karttunen, Jul 27 2014

Keywords

Links

Crossrefs

Inverse: A245604.
Cf. A026424, A028260, A066829, A055037, A055038.
Similar permutations: A143692, A244152, A244321, A245613, A245605, A245607.

Formula

a(1) = 1, and for n > 1, if A066829(n) = 1, then a(n) = 2 * A245603(A055038(n)), otherwise a(n) = 1 + (2 * A245603(A055037(n)-1)).
As a composition of related permutations:
a(n) = A244321(A245613(n)).
For all n >= 1, A000035(a(n)) = 1 - A066829(n). [Permutation A143692 has the same property.]

A245614 Permutation of natural numbers: a(1)=1; thereafter, if n is k-th number whose greatest prime factor has an odd index [i.e., n = A244991(k)], a(n) = A026424(a(k)), otherwise, when n is k-th number whose greatest prime factor has an even index [i.e., n = A244990(1+k)], a(n) = A028260(1+a(k)).

Original entry on oeis.org

1, 2, 4, 3, 7, 6, 10, 5, 9, 12, 11, 16, 15, 24, 18, 8, 17, 14, 22, 20, 26, 19, 29, 25, 28, 36, 35, 55, 39, 44, 31, 13, 30, 27, 21, 38, 34, 51, 46, 42, 37, 57, 40, 47, 32, 52, 45, 62, 56, 50, 68, 60, 82, 81, 67, 121, 86, 93, 105, 72, 65, 79, 33, 59, 64, 23, 53, 48, 41, 58, 49, 85, 71, 77, 66, 111, 99
Offset: 1

Views

Author

Antti Karttunen, Jul 27 2014

Keywords

Comments

This shares with the permutation A122111 the property that each term of A244990 is mapped to a unique term of A028260 and each term of A244991 is mapped to a unique term of A026424.

Links

Crossrefs

Inverse: A245613.
Cf. A026424, A028260, A066829, A244988, A244989, A244990, A244991, A244992, A122111.
Similar permutations: A244321, A244322, A245604, A227413, A237126, A243288, A243344, A243346, A245606.

Formula

a(1) = 1, and for n > 1, if A244992(n) = 1, a(n) = A026424(a(A244989(n))), otherwise a(n) = A028260(1+a(A244988(n)-1)).
As a composition of related permutations:
a(n) = A245604(A244321(n)).
For all n >= 1, A244992(n) = A066829(a(n)).
Showing 1-4 of 4 results.

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