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

Author

Antti Karttunen, Jun 01 2014

Keywords

• nonn

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

Crossrefs

Inverse: A243065.

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

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).