A100826 a(1) = 1; a(n+1) = gcd(n,a(n))-th smallest positive integer not already in the sequence.

1, 2, 4, 3, 5, 10, 7, 14, 8, 6, 11, 22, 12, 9, 13, 15, 16, 17, 18, 19, 20, 21, 23, 46, 25, 50, 26, 24, 30, 27, 31, 62, 29, 28, 33, 32, 37, 74, 35, 34, 38, 36, 44, 39, 40, 47, 41, 42, 52, 43, 45, 51, 48, 49, 53, 54, 56, 55, 57, 58, 60, 59, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71

Offset: 1

Author

Leroy Quet, Jan 06 2005

Keywords

• nonn

Comments

Probably a permutation of the positive integers.

This is a permutation iff, infinitely often, gcd(n, a(n)) = 1. Through n = 1000, gcd(n, a(n)) = 1 612 times, which is consistent with the natural conjecture that this is true with density 6/Pi^2 ~ 0.6079.... - Franklin T. Adams-Watters, Nov 28 2006

Links

• Franklin T. Adams-Watters, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A125628.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = Complement[ Range[250], Table[a[i], {i, n - 1}]][[GCD[n - 1, a[n - 1]]]]; Table[ a[n], {n, 60}] (* Robert G. Wilson v, Jan 10 2005 *)

Extensions

More terms from Robert G. Wilson v, Jan 10 2005