A251545 A251544, sorted.

4, 9, 21, 25, 26, 33, 58, 82, 85, 93, 95, 111, 115, 129, 177, 213, 237, 265, 267, 309, 321, 329, 335, 365, 381, 411, 427, 505, 519, 545, 565, 579, 581, 597, 633, 655, 679, 687, 699, 723, 753, 755, 785, 789, 831, 835, 879, 895, 921, 951, 973, 985, 1043, 1047, 1115, 1135

Offset: 1

Author

David Applegate and N. J. A. Sloane, Dec 16 2014

Keywords

• nonn

Comments

4, 9, and 25 are squares. It appears that all the remaining terms are the products of two distinct primes, usually both odd. (But not all such numbers occur, of course.)

It would be nice to have a characterization of these numbers that is independent of A098550.

Links

• 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 and J. Int. Seq. 18 (2015) 15.6.7.

Crossrefs

Cf. A098550, A251542-A251544, A253056.

Programs

Mathematica

terms = 56;
max = 15 terms;
f[lst_] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
A098550 = Nest[f, {1, 2, 3}, max - 3];
sel = Select[Transpose[{Range[max], A098550}], PrimeQ[#[[2]]]&][[All,1]]+2;
Sort[A098550[[sel]]][[1 ;; terms]] (* Jean-François Alcover, Sep 05 2018, after Robert G. Wilson v in A098550 *)