A098311 Smallest number not occurring earlier and coprime to a(ceiling(n/2)); a(1)=1.

1, 2, 3, 5, 4, 7, 6, 8, 9, 11, 10, 12, 13, 17, 15, 19, 14, 16, 18, 20, 21, 23, 25, 29, 22, 24, 26, 27, 28, 31, 30, 32, 33, 37, 35, 39, 41, 43, 47, 49, 34, 38, 36, 40, 42, 44, 45, 46, 51, 53, 55, 59, 57, 61, 50, 52, 65, 67, 48, 54, 71, 73, 63, 69, 56, 58, 60, 62, 64, 66, 68, 70

Offset

1,2

Comments

a(2*n) > a(2*n-1).

Permutation of the natural numbers with inverse A098313: A098312(n) = a(a(n)).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^12, showing records in red, local minima in blue, highlighting primes in green and other prime powers in gold.

Index entries for sequences that are permutations of the natural numbers

Mathematica

nn = 72; c[_] = False; Set[{a[1], c[1]}, {1, True}]; u = 2; Do[Set[{j, k}, {a[Ceiling[n/2]], u}]; While[Nand[! c[k], CoprimeQ[j, k]], k++]; Set[{a[n], c[k]}, {k, True}]; If[k == u, While[c[u], u++]], {n, 2, nn}]; Array[a, nn] (* Michael De Vlieger, Oct 28 2022 *)

Prog

(Haskell)
import Data.List ((\\))
a098311 n = a098311_list !! (n-1)
a098311_list = 1 : ys where
   ys = 2 : f ys [3..] where
        f (v:vs) ws = us ++ f vs (ws \\ us) where
          us = take 2 $ filter ((== 1) . (gcd v)) ws
-- Reinhard Zumkeller, Oct 11 2014

Crossrefs

Sequence in context: A351298 A082746 A098313 * A342265 A230086 A333404

Adjacent sequences: A098308 A098309 A098310 * A098312 A098313 A098314

Keyword

nonn

Author

Reinhard Zumkeller, Sep 02 2004

Extensions

Typo in definition fixed by Reinhard Zumkeller, Oct 11 2014

Status

approved