cp's OEIS Frontend

A269384 Permutation of natural numbers: a(1) = 1, a(n) = A255127(A001511(n), a(A003602(n))) - 1.

%I A269384 #8 Mar 03 2016 22:51:13
%S A269384 1,2,3,4,5,8,7,6,9,14,15,18,13,20,11,10,17,26,27,34,29,44,35,30,25,38,
%T A269384 39,48,21,32,19,12,33,50,51,64,53,80,67,58,57,86,87,108,69,104,59,54,
%U A269384 49,74,75,94,77,116,95,84,41,62,63,78,37,56,23,16,65,98,99,124,101,152,127,112,105,158,159,198,133,200
%N A269384 Permutation of natural numbers: a(1) = 1, a(n) = A255127(A001511(n), a(A003602(n))) - 1.
%C A269384 Permutation obtained from the Ludic sieve.
%C A269384 This sequence can be represented as a binary tree. For n > 2, each left hand child is obtained by doubling the contents of the parent node and subtracting one, and each right hand child is obtained by applying A269382(n), when the parent node contains n:
%C A269384                                     1
%C A269384                                     |
%C A269384                  ...................2...................
%C A269384                 3                                       4
%C A269384       5......../ \........8                   7......../ \........6
%C A269384      / \                 / \                 / \                 / \
%C A269384     /   \               /   \               /   \               /   \
%C A269384    /     \             /     \             /     \             /     \
%C A269384   9       14         15       18         13       20         11       10
%C A269384 17 26   27  34     29  44   35  30     25  38   39  48     21  32   19  12
%C A269384 etc.
%H A269384 Antti Karttunen, <a href="/A269384/b269384.txt">Table of n, a(n) for n = 1..8192</a>
%H A269384 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A269384 a(1) = 1, a(n) = A255127(A001511(n), a(A003602(n))) - 1.
%F A269384 a(1) = 1, a(2n) = A269382(a(n)), a(2n+1) = (2*a(n+1))-1.
%F A269384 Other identities. For all n >= 0:
%F A269384 A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]
%o A269384 (Scheme, two different implementations, both using memoization-macro definec)
%o A269384 (definec (A269384 n) (cond ((<= n 1) n) ((even? n) (A269382 (A269384 (/ n 2)))) (else (+ -1 (* 2 (A269384 (/ (+ n 1) 2)))))))
%o A269384 (definec (A269384 n) (cond ((<= n 1) n) (else (+ -1 (A255127bi (A001511 n) (A269384 (A003602 n))))))) ;; Code for A255127bi given in A255127.
%Y A269384 Inverse: A269383.
%Y A269384 Cf. A000035, A001511, A003602, A255127, A269382.
%Y A269384 Cf. also A269385, A269387 and also A249814, A269374.
%K A269384 nonn,tabf
%O A269384 1,2
%A A269384 _Antti Karttunen_, Mar 01 2016