A252754 Inverse of "Tree of Eratosthenes" permutation: a(1) = 0, after which, a(2n) = 1 + 2*a(n), a(2n+1) = 2 * a(A268674(2n+1)).

0, 1, 2, 3, 4, 5, 8, 7, 6, 9, 16, 11, 32, 17, 10, 15, 64, 13, 128, 19, 14, 33, 256, 23, 12, 65, 18, 35, 512, 21, 1024, 31, 22, 129, 20, 27, 2048, 257, 34, 39, 4096, 29, 8192, 67, 30, 513, 16384, 47, 24, 25, 26, 131, 32768, 37, 28, 71, 38, 1025, 65536, 43, 131072, 2049, 66, 63, 36, 45, 262144, 259, 46, 41, 524288, 55, 1048576, 4097, 130, 515, 40

Offset: 1

Author

Antti Karttunen, Jan 02 2015

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1024
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A252753.

Fixed points of a(n)+1: A253789.

Cf. A250470, A253556, A253557, A253558, A253559, A268674, A302041.

Similar permutations: A156552, A252756, A054429, A250246, A269388.

Differs from A156552 for the first time at n=21, where a(21) = 14, while A156552(21) = 18.

Programs

PARI

A252754(n) = if(1==n,0,if(!(n%2),1 + 2*A252754(n/2),2*A252754(A268674(n)))); \\ Antti Karttunen, Mar 31 2018

Scheme

;; With memoization-macro definec.
(definec (A252754 n) (cond ((= 1 n) (- n 1)) ((even? n) (+ 1 (* 2 (A252754 (/ n 2))))) (else (* 2 (A252754 (A250470 n))))))

Formula

a(1) = 0, after which, a(2n) = 1 + 2*a(n), a(2n+1) = 2 * a(A268674(2n+1)).

As a composition of related permutations:

a(n) = A054429(A252756(n)).

a(n) = A156552(A250246(n)).

From Antti Karttunen, Mar 31 2018: (Start)

A000120(a(n)) = A253557(n).

A069010(a(n)) = A302041(n).

A132971(a(n)) = A302050(n).

A106737(a(n)) = A302051(n).

(End)

Extensions

Name edited and formula corrected by Antti Karttunen, Mar 31 2018