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

1,2

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

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].

Prog

(Scheme, with memoization-macro definec)
(definec (A246678 n) (cond ((<= n 1) n) ((odd? n) (+ 1 (* 2 (A246678 (/ (- n 1) 2))))) (else (+ -1 (A242378bi (A007814 n) (+ 1 (A000265 n)))))))  ;; Code for A242378bi given in A242378.

Crossrefs

Inverse: A246677.

Variants: A246676, A246684.

Even bisection halved: A246680.

Cf. A000265, A001511, A003961, A242378.

Sequence in context: A082314 A249811 A246676 * A269384 A249814 A246684

Adjacent sequences: A246675 A246676 A246677 * A246679 A246680 A246681

Keyword

nonn

Author

Antti Karttunen, Sep 01 2014

Status

approved