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A243288 Permutation of natural numbers: a(1)=1, a(2n) = A102750(a(n)), a(2n+1) = A070003(a(n)).

%I A243288 #24 Jan 21 2020 01:31:07
%S A243288 1,2,4,3,8,6,16,5,9,12,32,10,25,22,81,7,18,13,36,17,54,42,242,14,49,
%T A243288 34,150,30,128,99,882,11,27,24,100,19,64,46,256,23,98,68,490,55,338,
%U A243288 279,4624,20,72,62,432,44,245,178,2209,40,216,154,1800,119,1200,966
%N A243288 Permutation of natural numbers: a(1)=1, a(2n) = A102750(a(n)), a(2n+1) = A070003(a(n)).
%C A243288 This is an instance of "entanglement permutation", where two pairs of complementary subsets of natural numbers are interwoven with each other. In this case complementary pair odd/even numbers (A005408/A005843) is entangled with complementary pair A070003/A102750 (numbers which are divisible/not divisible by the square of their largest prime factor).
%C A243288 Thus this shares with the permutation A122111 the property that each even number is mapped to a unique term of A102750 and each odd number (larger than 1) to a unique term of A070003.
%H A243288 Antti Karttunen, <a href="/A243288/b243288.txt">Table of n, a(n) for n = 1..94</a>
%H A243288 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A243288 a(1)=1, and for n > 1, if n=2k, a(n) = A102750(a(k)), otherwise, when n = 2k+1, a(n) = A070003(a(k)).
%o A243288 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A243288 (definec (A243288 n) (cond ((<= n 1) n) ((even? n) (A102750 (A243288 (/ n 2)))) (else (A070003 (A243288 (/ (- n 1) 2))))))
%Y A243288 Inverse of A243287.
%Y A243288 Cf. A005843, A005408, A070003, A102750, A243282, A243285, A241917, A122111.
%Y A243288 Similarly constructed permutations: A243343-A243346, A135141-A227413, A237126-A237427, A193231.
%K A243288 nonn
%O A243288 1,2
%A A243288 _Antti Karttunen_, Jun 02 2014