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

1,2

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

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 *)

Prog

(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

Crossrefs

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

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

Sequence in context: A154444 A154443 A180200 * A132196 A153150 A069766

Adjacent sequences: A121213 A121214 A121215 * A121217 A121218 A121219

Keyword

nonn

Author

Leroy Quet, Aug 20 2006

Extensions

Extended by Ray Chandler, Aug 22 2006

Status

approved