A243066 Permutation of natural numbers, the even bisection of A241909 incremented by one and halved; equally, a composition of A241909 and A048673: a(n) = A048673(A241909(n)).

1, 2, 5, 3, 14, 13, 41, 4, 8, 63, 122, 25, 365, 313, 38, 6, 1094, 18, 3281, 172, 188, 1563, 9842, 61, 23, 7813, 11, 1201, 29525, 123, 88574, 7, 938, 39063, 113, 39, 265721, 195313, 4688, 666, 797162, 858, 2391485, 8404, 74, 976563, 7174454, 85, 68, 88, 23438, 58825, 21523361, 28

Offset

1,2

Comments

For n > 1, 2n is found in A241909 from the position (2*a(n))-1. I.e., A241909((2*a(n))-1) = 2n for all n >= 2.

Or in other words, a(n) gives the position in the odd bisection of A241909 where 2n is located at.

Are there any other fixed points than 1, 2, 18 and 72?

Links

Antti Karttunen, Table of n, a(n) for n = 1..512

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(n) = (A241909(2*n)+1)/2.

As a composition of related permutations:

a(n) = A048673(A241909(n)).

a(n) = A241909(A243062(A241909(n))).

For all n>=1, a(2^n) = A006254(n).

Prog

(Scheme, two alternatives)
(define (A243066 n) (if (= n 1) 1 (/ (+ 1 (A241909 (* 2 n))) 2)))
(define (A243066 n) (A048673 (A241909 n)))

Crossrefs

Inverse: A243065.

Cf. A048673, A241909, A243505-A243506, A244152-A244154, A243061-A243062.

Sequence in context: A341351 A285742 A245612 * A368316 A181921 A282575

Adjacent sequences: A243063 A243064 A243065 * A243067 A243068 A243069

Keyword

nonn

Author

Antti Karttunen, Jun 01 2014

Status

approved