A246678 Permutation of natural numbers: a(1) = 1, a(2n+1) = 1 + 2*a(n), a(2n) = A242378(A001511(n), (1+A000265(n))) - 1.

1, 2, 3, 4, 5, 8, 7, 6, 9, 14, 11, 24, 17, 26, 15, 10, 13, 20, 19, 34, 29, 44, 23, 48, 49, 32, 35, 124, 53, 80, 31, 12, 21, 74, 27, 54, 41, 62, 39, 76, 69, 38, 59, 174, 89, 134, 47, 120, 97, 50, 99, 64, 65, 98, 71, 342, 249, 104, 107, 624, 161, 242, 63, 16, 25, 56, 43, 244, 149, 224, 55, 90, 109, 68, 83

Offset: 1

Author

Antti Karttunen, Sep 01 2014

Keywords

• nonn

Comments

See the comments in A246676. This is a similar permutation, except for odd numbers, which are here recursively permuted by the emerging permutation itself. The even bisection halved gives A246680, the odd bisection from a(3) onward with one subtracted and then halved gives this sequence back.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8192
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A246677.

Variants: A246676, A246684.

Even bisection halved: A246680.

Cf. A000265, A001511, A003961, A242378.

Formula

a(1) = 1, a(2n+1) = 1 + 2*a(n), a(2n) = A242378(A001511(n), (1+A000265(n))) - 1. [Where the bivariate function A242378(k,n) changes each prime p(i) in the prime factorization of n to p(i+k), i.e., it's the result of A003961 iterated k times starting from n].