A123923 a(1)=1. a(n) = (highest term among first n-1 terms of sequence which divides n)-th integer from among those integers not occurring among the first n-1 terms of the sequence.

1, 2, 3, 5, 9, 7, 13, 6, 17, 12, 4, 23, 25, 18, 15, 14, 33, 35, 8, 20, 24, 11, 45, 47, 49, 34, 29, 38, 57, 40, 10, 30, 65, 67, 69, 48, 16, 75, 42, 79, 19, 83, 21, 43, 89, 61, 93, 95, 97, 64, 54, 50, 22, 107, 46, 55, 113, 78, 26, 82, 121, 28, 71, 127, 129, 90, 133, 92, 137, 96

Offset

1,2

Comments

Sequence is likely a permutation of the positive integers.

Links

Ivan Neretin, Table of n, a(n) for n = 1..10000

Example

3 is the largest integer which occurs among the first 5 terms of the sequence and which divides 6. So for a(6) we want the 3rd integer from among those positive integers not among the first 5 terms of the sequence (i.e. we want the 3rd integer from among 4,6,7,8,10,...). So a(6) = 7.

Mathematica

f[l_List] := Block[{k = 0, c = Max @@ Select[l, Mod[Length[l] + 1, # ] == 0 &]}, While[c > 0, k++; While[MemberQ[l, k], k++ ]; c--; ]; Append[l, k]]; Nest[f, {1}, 72] (* Ray Chandler, Nov 23 2006 *)
Fold[Append[#1, Complement[Range[Max@#1 + (r = Max@Intersection[#1, Divisors@#2])], #1][[r]]] &, {1}, Range[2, 70]] (* Ivan Neretin, Oct 20 2018 *)

Crossrefs

Sequence in context: A342444 A011026 A069805 * A045965 A323390 A346096

Adjacent sequences: A123920 A123921 A123922 * A123924 A123925 A123926

Keyword

nonn

Author

Leroy Quet, Nov 20 2006

Extensions

Extended by Ray Chandler, Nov 23 2006

Status

approved