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

1,2

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

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 *)

Crossrefs

Cf. A125628.

Sequence in context: A091449 A100834 A264996 * A338161 A232799 A276472

Adjacent sequences: A100823 A100824 A100825 * A100827 A100828 A100829

Keyword

nonn

Author

Leroy Quet, Jan 06 2005

Extensions

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

Status

approved