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A256224 a(n) = n if n <= 3, otherwise a(n) is the smallest number not occurring earlier such that gcd(a(n-2), a(n)) is a prime or a power of a prime (but not 1) and gcd(a(n-1), a(n))=1.

%I A256224 #29 Oct 27 2023 22:11:26
%S A256224 1,2,3,4,9,8,15,14,5,6,25,16,35,12,7,10,21,22,27,11,18,55,26,33,13,24,
%T A256224 65,28,39,20,51,32,17,30,119,38,49,19,42,95,34,45,44,57,40,63,46,75,
%U A256224 23,36,115,52,69,50,81,56,87,62,29,31,58,93,64,99,68,77,48
%N A256224 a(n) = n if n <= 3, otherwise a(n) is the smallest number not occurring earlier such that gcd(a(n-2), a(n)) is a prime or a power of a prime (but not 1) and gcd(a(n-1), a(n))=1.
%C A256224 The sequence is infinite.
%C A256224 Conjecture: This is a permutation of the natural numbers.
%H A256224 Alois P. Heinz, <a href="/A256224/b256224.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Peter J. C. Moses)
%H A256224 David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, <a href="http://arxiv.org/abs/1501.01669">The Yellowstone Permutation</a>, arXiv preprint arXiv:1501.01669, 2015.
%t A256224 a[n_] := a[n] = If[n <= 3, n, For[k = 1, True, k++, If[FreeQ[Array[a, n-1], k], g = GCD[a[n-2], k]; If[g>1 && PrimeNu[g] == 1 && GCD[a[n-1], k] == 1, Return[k]]]]];
%t A256224 Array[a, 100] (* _Jean-François Alcover_, Aug 06 2018 *)
%Y A256224 Cf. A098550, A256189.
%K A256224 nonn
%O A256224 1,2
%A A256224 _Vladimir Shevelev_, Mar 19 2015
%E A256224 More terms from _Peter J. C. Moses_, Mar 24 2015