A246677 Permutation of natural numbers: a(1) = 1, a(2n) = A000079(A055396(2n+1)-1) * ((2*A246277(2n+1))-1), a(2n+1) = 1 + 2*a(n).

1, 2, 3, 4, 5, 8, 7, 6, 9, 16, 11, 32, 17, 10, 15, 64, 13, 128, 19, 18, 33, 256, 23, 12, 65, 14, 35, 512, 21, 1024, 31, 26, 129, 20, 27, 2048, 257, 42, 39, 4096, 37, 8192, 67, 22, 513, 16384, 47, 24, 25, 50, 131, 32768, 29, 36, 71, 66, 1025, 65536, 43, 131072, 2049, 38, 63, 52, 53, 262144, 259, 74, 41

Offset

1,2

Comments

See the comments in A246675. This is otherwise similar permutation, except for odd numbers, which are here recursively permuted by the emerging permutation itself. The even bisection halved gives A246679, 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..2048

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(2n) = A000079(A055396(2n+1)-1) * ((2*A246277(2n+1))-1), a(2n+1) = 1 + 2*a(n).

Prog

(Scheme, with memoization-macro definec)
(definec (A246677 n) (cond ((<= n 1) n) ((odd? n) (+ 1 (* 2 (A246677 (/ (- n 1) 2))))) (else (* (A000079 (- (A055396 (+ 1 n)) 1)) (-1+ (* 2 (A246277 (+ 1 n))))))))

Crossrefs

Inverse: A246678. Variants: A246675, A246683.

Even bisection halved: A246679.

Cf. A000079, A055396, A246277.

a(n) differs from A156552(n+1) for the first time at n=32, where a(32) = 26, while A156552(33) = 34.

Sequence in context: A246675 A269388 A252754 * A156552 A269383 A249813

Adjacent sequences: A246674 A246675 A246676 * A246678 A246679 A246680

Keyword

nonn

Author

Antti Karttunen, Sep 01 2014

Status

approved