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%I #11 May 12 2024 15:35:49
%S 1,3,2,7,5,12,4,10,19,8,16,6,27,14,24,11,37,21,9,33,18,49,30,15,44,26,
%T 13,62,40,23,57,36,20,77,52,32,17,71,47,29,93,66,43,25,87,60,39,111,
%U 22,81,55,35,104,75,51,131,31,98,69,46,123,28,91,64,152,42
%N If the n-th 3-smooth number, A003586(n), equals 2^i * 3^j for some i, j >= 0, then the a(n)-th 3-smooth number, A003586(a(n)), equals 2^j * 3^i.
%C This sequence is a self-inverse permutation of the positive integers with infinitely many fixed points (A202821).
%H Rémy Sigrist, <a href="/A372744/b372744.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A372744/a372744.gp.txt">PARI program</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A022328(a(n)) = A022329(n).
%F A022329(a(n)) = A022328(n).
%F a(n) = n iff n belongs to A202821.
%F sign(a(n) - n) = sign(A022328(n) - A022329(n)).
%e A003586(8) = 12 = 2^2 * 3^1, A003586(10) = 18 = 2^1 * 3^2, so a(8) = 10 and.
%o (PARI) \\ See Links section.
%Y Cf. A003586, A022328, A022329, A202821 (fixed points).
%K nonn
%O 1,2
%A _Rémy Sigrist_, May 12 2024