A121216 a(1)=1, a(2) = 2; thereafter a(n) = the smallest positive integer which does not occur earlier in the sequence and which is coprime to a(n-2).

1, 2, 3, 5, 4, 6, 7, 11, 8, 9, 13, 10, 12, 17, 19, 14, 15, 23, 16, 18, 21, 25, 20, 22, 27, 29, 26, 24, 31, 35, 28, 32, 33, 37, 34, 30, 39, 41, 38, 36, 43, 47, 40, 42, 49, 53, 44, 45, 51, 46, 50, 55, 57, 48, 52, 59, 61, 54, 56, 65, 67, 58, 60, 63, 71, 62, 64, 69, 73, 68, 66, 75

Offset: 1

Author

Leroy Quet, Aug 20 2006

Keywords

• nonn

Comments

Permutation of the positive natural numbers with inverse A225047: a(A225047(n)) = A225047(a(n)) = n. - Reinhard Zumkeller, Apr 25 2013

I confirm that this is a permutation. - N. J. A. Sloane, Mar 28 2015 [This can be proved using an argument similar to (but simpler than) the proof in A093714. - N. J. A. Sloane, May 05 2022]

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A084937, A121217, A225047, A098550, A256219 (positions of primes), A256399.

See also A352933, A352934, A352935, A352936, A352937, A353705, A353707, A353708.

Programs

Haskell

import Data.List (delete, (\\))
a121216 n = a121216_list !! (n-1)
a121216_list = 1 : 2 : f 1 2 [3..] where
f x y zs = g zs where
  g (u:us) = if gcd x u == 1 then h $ delete u zs else g us where
   h (v:vs) = if gcd y v == 1 then u : v : f u v (zs \\ [u,v]) else h vs
-- Reinhard Zumkeller, Apr 25 2013

Mathematica

Nest[Append[#, Block[{k = 3}, While[Nand[FreeQ[#, k], GCD[#[[-2]], k] == 1], k++]; k]] &, {1, 2}, 70] (* Michael De Vlieger, Dec 26 2019 *)

Extensions

Extended by Ray Chandler, Aug 22 2006