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

1,2

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.

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 *)

Crossrefs

Cf. A098550, A256189.

Sequence in context: A098550 A335585 A344176 * A340783 A255509 A257862

Adjacent sequences: A256221 A256222 A256223 * A256225 A256226 A256227

Keyword

nonn

Author

Vladimir Shevelev, Mar 19 2015

Extensions

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

Status

approved