A245613 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) = A244991(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) = A244990(1+a(k)).

1, 2, 4, 3, 8, 6, 5, 16, 9, 7, 11, 10, 32, 18, 13, 12, 17, 15, 22, 20, 35, 19, 66, 14, 24, 21, 34, 25, 23, 33, 31, 45, 63, 37, 27, 26, 41, 36, 29, 43, 69, 40, 134, 30, 47, 39, 44, 68, 71, 50, 38, 46, 67, 131, 28, 49, 42, 70, 64, 52, 92, 48, 127, 65, 61, 75, 55, 51, 89, 83, 73, 60

Offset: 1

Author

Antti Karttunen, Jul 27 2014

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Inverse: A245614.

Cf. A026424, A028260, A055037, A055038, A066829, A244990, A244991, A244992, A122111.

Similar entanglement permutations: A243287, A243343, A243345, A244321-A244322, A245603, A135141, A237427, A245605.

Formula

a(1) = 1, and for n > 1, if A066829(n) = 1, a(n) = A244991(a(A055038(n))), otherwise a(n) = A244990(1+a(A055037(n)-1)).

As a composition of related permutations:

a(n) = A244322(A245603(n)).

For all n >= 1, A066829(n) = A244992(a(n)).