A251604 A Zumkeller-type sequence (cf. A098550): a(n) = n if n <= 3, otherwise the smallest number not occurring earlier having at least one common factor with a(n-2)+a(n-1), but none with a(n-1).

1, 2, 3, 5, 4, 9, 13, 6, 19, 10, 29, 12, 41, 53, 8, 61, 15, 14, 87, 101, 16, 21, 37, 18, 11, 58, 23, 24, 47, 71, 20, 7, 27, 17, 22, 39, 122, 35, 157, 26, 33, 59, 28, 45, 73, 30, 103, 38, 51, 89, 25, 32, 57, 178, 55, 233, 34, 63, 97, 36, 49, 40, 267, 307, 42

Offset: 1

Author

Vladimir Shevelev, Dec 13 2014

Keywords

• nonn

Comments

Conjectured to be a permutation of the positive integers.

See also A255972 for this conjecture. - Reinhard Zumkeller, Mar 12 2015

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..5000
• 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 and J. Int. Seq. 18 (2015) 15.6.7.

Crossrefs

Cf. A098550.

Cf. A255972.

Programs

Haskell

import Data.List (delete)
a251604 n = a251604_list !! (n-1)
a251604_list = 1 : 2 : 3 : f 2 3 [4..] where
   f u v ws = g ws where
     g (x:xs) = if gcd x (u + v) > 1 && gcd x v == 1
                   then x : f v x (delete x ws) else g xs
-- Reinhard Zumkeller, Mar 12 2015

Mathematica

a[n_] := a[n] = If[n <= 3, n, For[k = 1, True, k++, If[FreeQ[Array[a, n-1], k], If[!CoprimeQ[k, a[n-2]+a[n-1]] && CoprimeQ[k, a[n-1]], Return[k]]]]];
Array[a, 65] (* Jean-François Alcover, Jul 31 2018 *)

Extensions

More terms from Peter J. C. Moses, Dec 13 2014