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

Author

Leroy Quet, Dec 22 2006

Keywords

• nonn

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

Examples

			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.
		

Links

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

Programs

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 *)

Extensions

Extended by Ray Chandler, Dec 24 2006