A255509 a(1)=1, a(2)=2, a(3)=3; for n>=4, a(n) is the maximal prime factor P_n of a(n-2) if P_n is not already a term, otherwise a(n) is the smallest not appeared earlier positive number x such that gcd(x,a(n-2))>1, gcd(x,a(n-1))=1.

1, 2, 3, 4, 9, 8, 15, 14, 5, 7, 10, 21, 16, 27, 20, 33, 25, 11, 30, 77, 6, 35, 12, 49, 18, 91, 22, 13, 24, 65, 28, 39, 32, 45, 26, 51, 38, 17, 19, 34, 57, 40, 63, 44, 69, 50, 23, 36, 115, 42, 55, 46, 75, 52, 81, 56, 87, 62, 29, 31, 58, 93, 64, 99, 68, 105, 74

Offset: 1

Author

Vladimir Shevelev, Feb 24 2015

Keywords

• nonn

Comments

By definition, in contrast to A098550, in this sequence there is a priority for appearance of the primes.

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..1000
• David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669 [math.NT], 2015.

Crossrefs

Cf. A098550, A247225, A247942, A249167, A251604, A254077.

Programs

Mathematica

a[n_] := a[n] = If[n <= 3, n, Module[{p = FactorInteger[a[n-2]][[-1, 1]], aa = Array[a, n-1], x}, If[FreeQ[aa, p], Return[p], For[x = 4, True, x++, If[FreeQ[aa, x] && GCD[x, a[n-2]]>1 && GCD[x, a[n-1]]==1, Return[x]]]]]];
Array[a, 100] (* Jean-François Alcover, Oct 06 2018 *)

Extensions

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