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.

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, 65, 28, 39, 20, 51, 32, 17, 30, 119, 38, 49, 19, 42, 95, 34, 45, 44, 57, 40, 63, 46, 75, 23, 36, 115, 52, 69, 50, 81, 56, 87, 62, 29, 31, 58, 93, 64, 99, 68, 77, 48

Offset: 1

Author

Vladimir Shevelev, Mar 19 2015

Keywords

• nonn

Comments

The sequence is infinite.

Conjecture: This is a permutation of the natural numbers.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Peter J. C. Moses)
• David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669, 2015.

Crossrefs

Cf. A098550, A256189.

Programs

Mathematica

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]]]]];
Array[a, 100] (* Jean-François Alcover, Aug 06 2018 *)

Extensions

More terms from Peter J. C. Moses, Mar 24 2015