A125060 Irregular array where a(1)=1; run n of the sequence is the first a(n-1) integers from among those positive integers which are coprime to n and which do not occur earlier in the sequence {a(k)}.

1, 3, 2, 4, 5, 7, 9, 6, 8, 11, 12, 13, 17, 19, 23, 25, 10, 15, 16, 18, 20, 22, 24, 21, 27, 29, 31, 33, 35, 37, 39, 41, 14, 26, 28, 32, 34, 38, 43, 47, 49, 51, 53, 57, 59, 61, 30, 36, 40, 42, 45, 46, 48, 50, 52, 54, 56, 55, 65, 67, 71, 73, 77, 79, 83, 85, 89, 91, 95, 44, 58, 60

Offset

1,2

Comments

This sequence is a permutation of the positive integers.

Links

Table of n, a(n) for n=1..72.

Example

The sequence grouped by runs, where run n, after the first 1, consists of a(n-1) terms:
1,(3),(2,4,5),(7,9),(6,8,11,12),(13,17,19,23,25),(10,15,16,18,20,22,24),...
a(5) is 5. So run 6 contains the first 5 positive integers which do not occur earlier in the sequence and which are coprime to 6, (13,17,19,23,25).

Mathematica

f[l_List] := Block[{n = Length[l] + 1, fl = Flatten[l], c, k = 0, r = {}}, c = fl[[n - 1]]; While[c > 0, k++; While[MemberQ[fl, k] || GCD[k, n] > 1, k++ ]; AppendTo[r, k]; c--; ]; Append[l, r]]; Nest[f, {{1}}, 12] // Flatten (* Ray Chandler, Feb 13 2007 *)

Crossrefs

Cf. A081964.

Sequence in context: A364839 A165279 A345866 * A039882 A370803 A326357

Adjacent sequences: A125057 A125058 A125059 * A125061 A125062 A125063

Keyword

nonn

Author

Leroy Quet, Jan 08 2007

Extensions

Extended by Ray Chandler, Feb 13 2007

Status

approved