A124653 a(1)=1. a(2)=2. a(n) = smallest positive integer not occurring earlier in the sequence such that every positive integer <= and coprime to (a(n-1)+a(n-2)) is also coprime to a(n).

1, 2, 3, 5, 4, 9, 13, 8, 7, 15, 11, 16, 27, 43, 10, 53, 21, 32, 59, 49, 6, 25, 31, 14, 45, 61, 64, 125, 63, 47, 20, 67, 29, 12, 41, 71, 28, 33, 73, 106, 179, 19, 18, 37, 55, 23, 24, 79, 103, 26, 81, 107, 94, 201, 295, 62, 17, 83, 40, 123, 163, 22, 185, 69, 127, 56, 183, 239

Offset

1,2

Comments

Is this sequence a permutation of the positive integers?

Links

Table of n, a(n) for n=1..68.

Example

a(6)+a(7) = 22. The positive integers <= 22 and coprime to 22 are 1,3,5,7,9,13,15, 17,19,21. The smallest positive integer not occurring among the first 7 terms of the sequence which is coprime to 1,3,5,7,9,13,15,17,19, 21 is 8. (7 does not occur among the first 7 terms of {a(k)}, but 7 is not coprime to 7.) So a(8) = 8.

Mathematica

f[n_] := Select[Range[n], GCD[ #, n] == 1 &]; g[l_List] := Block[{k = 1, t = f[l[[ -1]] + l[[ -2]]]}, While[MemberQ[l, k] || Times @@ GCD[t, k] > 1, k++ ]; Append[l, k]]; Nest[g, {1, 2}, 66] (* Ray Chandler, Dec 24 2006 *)

Crossrefs

Sequence in context: A307023 A307024 A349493 * A365642 A353082 A085947

Adjacent sequences: A124650 A124651 A124652 * A124654 A124655 A124656

Keyword

nonn

Author

Leroy Quet, Dec 22 2006

Extensions

Extended by Ray Chandler, Dec 24 2006

Status

approved