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Permutation of natural numbers: a(1)=1, a(2n) = A102750(a(n)), a(2n+1) = A070003(a(n)).
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%I #24 Jan 21 2020 01:31:07

%S 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 34,150,30,128,99,882,11,27,24,100,19,64,46,256,23,98,68,490,55,338,

%U 279,4624,20,72,62,432,44,245,178,2209,40,216,154,1800,119,1200,966

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

%C 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 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 Antti Karttunen, <a href="/A243288/b243288.txt">Table of n, a(n) for n = 1..94</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F 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 (Scheme, with _Antti Karttunen_'s IntSeq-library)

%o (definec (A243288 n) (cond ((<= n 1) n) ((even? n) (A102750 (A243288 (/ n 2)))) (else (A070003 (A243288 (/ (- n 1) 2))))))

%Y Inverse of A243287.

%Y Cf. A005843, A005408, A070003, A102750, A243282, A243285, A241917, A122111.

%Y Similarly constructed permutations: A243343-A243346, A135141-A227413, A237126-A237427, A193231.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 02 2014