A124652 a(1)=1. a(n) = smallest positive integer not occurring earlier in the sequence such that every positive integer <= and coprime to (sum{k=1 to n-1} a(k)) is also coprime to a(n).

1, 2, 3, 4, 5, 9, 6, 8, 16, 12, 11, 7, 14, 28, 18, 24, 21, 27, 32, 31, 81, 10, 20, 13, 169, 22, 33, 19, 17, 39, 26, 49, 37, 44, 36, 48, 54, 64, 25, 35, 40, 29, 41, 15, 45, 30, 50, 80, 58, 52, 60, 72, 47, 1369, 42, 56, 98, 59, 57, 38, 76, 62, 116, 128, 75, 87, 23, 115, 46, 91

Offset

1,2

Comments

Is this sequence a permutation of the positive integers?

Alternatively, let a(1) = 1 and S = Sum_{i=1..n-1} a(i); a(n) = smallest positive k != a(i), i < n, such that all primes p | k also either divide or exceed S. - Michael De Vlieger, Apr 22 2024

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

The sum of the first 7 terms of the sequence is 30. The positive integers <= 30 and coprime to 30 are 1,7,11,13,17,19,23,29. The smallest positive integer not occurring among the first 7 terms of the sequence which is coprime to 1,7,11,13,17,19,23,29 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[Plus @@ l]}, While[MemberQ[l, k] || Times @@ GCD[t, k] > 1, k++ ]; Append[l, k]]; Nest[g, {1}, 70] (* Ray Chandler, Dec 24 2006 *)

Crossrefs

Sequence in context: A246279 A285112 A253565 * A250552 A048623 A262692

Adjacent sequences: A124649 A124650 A124651 * A124653 A124654 A124655

Keyword

nonn

Author

Leroy Quet, Dec 22 2006

Extensions

Extended by Ray Chandler, Dec 24 2006

Status

approved