A269388 Permutation of natural numbers: a(1) = 0, after which, a(2n) = 1 + 2*a(n), a(2n+1) = 2 * a(A269380(n)).

0, 1, 2, 3, 4, 5, 8, 7, 6, 9, 16, 11, 32, 17, 10, 15, 64, 13, 12, 19, 14, 33, 128, 23, 256, 65, 18, 35, 512, 21, 24, 31, 22, 129, 20, 27, 1024, 25, 34, 39, 2048, 29, 4096, 67, 30, 257, 8192, 47, 28, 513, 26, 131, 16384, 37, 48, 71, 38, 1025, 40, 43, 32768, 49, 66, 63, 36, 45, 65536, 259, 46, 41, 131072, 55, 96, 2049, 130, 51, 262144, 69, 44

Offset

1,3

Comments

Note the indexing: Domain starts from 1, range from 0.

Links

Antti Karttunen, Table of n, a(n) for n = 1..1024

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 0, after which, a(2n) = 1 + 2*a(n), a(2n+1) = 2 * a(A269380(n)).

As a composition of other permutations:

a(n) = A252754(A269172(n)).

a(n) = A269378(A260742(n)).

Prog

(Scheme, with memoization-macro definec)
(definec (A269388 n) (cond ((= 1 n) (- n 1)) ((even? n) (+ 1 (* 2 (A269388 (/ n 2))))) (else (* 2 (A269388 (A269380 n))))))

Crossrefs

Inverse: A269387.

Cf. A269380.

Related permutations: A260742, A269386, A269172.

Cf. also A252754, A269378.

Differs from A156552, A252754 and A246677(n-1) for the first time at n=19, which here a(19)=12, instead of 128.

Sequence in context: A246684 A249812 A246675 * A252754 A246677 A156552

Adjacent sequences: A269385 A269386 A269387 * A269389 A269390 A269391

Keyword

nonn

Author

Antti Karttunen, Mar 01 2016

Status

approved