A245606 -id:A245606 - cp's OEIS frontend

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)).

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

Antti Karttunen, Jul 27 2014

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.

Antti Karttunen, Table of n, a(n) for n = 1..10001
Index entries for sequences that are permutations of the natural numbers

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

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)).

A269864 Permutation of natural numbers: a(1) = 1, a(2n) = A269360(a(n)), a(2n+1) = A250469(1+a(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 9, 10, 7, 8, 15, 16, 11, 26, 27, 28, 13, 12, 21, 22, 25, 36, 45, 46, 19, 14, 33, 76, 65, 66, 81, 82, 31, 18, 39, 34, 17, 56, 63, 64, 29, 50, 75, 106, 41, 116, 135, 136, 53, 24, 57, 40, 35, 86, 99, 226, 143, 120, 195, 196, 71, 206, 243, 244, 89, 38, 93, 52, 23, 96, 117, 100, 77, 20, 51, 166, 145, 156, 189, 190, 119, 32, 87

Offset: 1

Antti Karttunen, Mar 13 2016

This sequence can be represented as a binary tree. When the parent contains n, the left hand child contains A269360(n) [= 1+A250469(n)] and the right hand child contains A250469(1+n):
                                     1
                                     |
                  ................../ \..................
                 2                                       3
       4......../ \........5                   6......../ \........9
      / \                 / \                 / \                 / \
     /   \               /   \               /   \               /   \
    /     \             /     \             /     \             /     \
  10       7           8       15         16       11         26       27
28  13   12 21       22 25   36  45     46  19   14  33     76  65   66  81
etc.

Antti Karttunen, Table of n, a(n) for n = 1..5887
Index entries for sequences that are permutations of the natural numbers

Inverse: A269863.
Cf. A250469, A269360.
Cf. also A269865, A269866, A269867.
Differs from similarly constructed A245606 for the first time at n=15, where a(15)=27 instead of 21.

a(1) = 1, a(2n) = 1 + A250469(a(n)), a(2n+1) = A250469(1+a(n)).

A245712 Permutation of natural numbers, odd bisection of A245706 incremented by one and halved: a(n) = (1+A245706((2*n)-1)) / 2.

Original entry on oeis.org

1, 2, 3, 6, 4, 14, 5, 38, 10, 8, 26, 330, 18, 46, 283, 42, 11, 34, 7, 50, 70, 22, 17, 326, 37, 58, 27, 32, 53, 9590, 554, 4438, 278, 174, 9, 16, 15, 142, 25, 226, 146, 658, 105, 310, 1190, 806, 1770, 524, 51, 5258, 66, 5302, 35, 518, 17739, 1054, 19030, 542, 5550, 8054, 35498, 4434, 29, 810, 1106, 72, 75, 28, 63, 166, 83, 150, 44

Offset: 1

Antti Karttunen, Jul 30 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10001
Index entries for sequences that are permutations of the natural numbers

Inverse: A245711.

Cf. A245706, A245606.

A245712(n) =(1+A245706((2*n)-1))/2;
for(n=1, 10001, write("b245712.txt", n, " ", A245712(n)));
\\ For the rest of code, see under A245706.

(define (A245712 n) (/ (+ 1 (A245706 (+ n n -1))) 2))

a(n) = (1+A245706((2*n)-1)) / 2.

cp's OEIS Frontend

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)).

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A269864 Permutation of natural numbers: a(1) = 1, a(2n) = A269360(a(n)), a(2n+1) = A250469(1+a(n)).

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A245712 Permutation of natural numbers, odd bisection of A245706 incremented by one and halved: a(n) = (1+A245706((2*n)-1)) / 2.

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