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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. 3

%I

%S 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 65,28,39,20,51,32,17,30,119,38,49,19,42,95,34,45,44,57,40,63,46,75,

%U 23,36,115,52,69,50,81,56,87,62,29,31,58,93,64,99,68,77,48

%N 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 The sequence is infinite.

%C Conjecture: This is a permutation of the natural numbers.

%H Peter J. C. Moses and 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 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 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 Array[a, 100] (* _Jean-Fran├žois Alcover_, Aug 06 2018 *)

%Y Cf. A098550, A256189.

%K nonn

%O 1,2

%A _Vladimir Shevelev_, Mar 19 2015

%E More terms from _Peter J. C. Moses_, Mar 24 2015

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Last modified September 21 07:06 EDT 2020. Contains 337267 sequences. (Running on oeis4.)