A118784 a(0) = 1; a(n) = (number of earlier terms of the sequence which are coprime to n)th positive integer not among the earlier terms of the sequence.

1, 2, 3, 5, 7, 9, 8, 13, 14, 16, 12, 22, 11, 25, 19, 24, 23, 34, 21, 37, 28, 32, 30, 45, 27, 46, 36, 43, 38, 58, 26, 62, 42, 52, 44, 60, 33, 73, 49, 61, 50, 82, 39, 85, 56, 70, 59, 94, 51, 89, 64, 83, 68, 106, 55, 96, 71, 95, 78, 117, 53, 121, 86, 100, 87, 111, 66, 134, 90, 112

Offset

0,2

Links

Ivan Neretin, Table of n, a(n) for n = 0..10000

Example

The first 8 terms of the sequence (a(0) through a(7)) are 1,2,3,5,7,9,8,13. Of these there are 6 terms that are coprime to 8 (those terms being 1, 3, 5, 7, 9 and 13). So a(8) is the 6th positive integer missing from the first 8 terms of the sequence (i.e., is the 6th integer of the sequence 4, 6, 10, 11, 12, 14, 15, 16, ...). So a(8) = 14.

Mathematica

a = {1}; Do[AppendTo[a, Complement[Range[2 Max@a], a][[Length@Select[a, GCD[#, n] == 1 &]]]], {n, 69}]; a (* Ivan Neretin, Feb 26 2018 *)

Prog

(Magma) find:=function(S, k) c:=0; j:=0; while j lt #S and c lt k do j+:=1; if S[j] eq 0 then c+:=1; end if; end while; if c eq k then return j; else return 0; end if; end function;
z:=150; m:=70; W:=[ 0: n in [1..z] ]; V:=[1]; W[1]:=1; for n in [1..m] do c:=#[ j: j in [1..#V] | Gcd(n, V[j]) eq 1 ]; a:=find(W, c); if a eq 0 then break; end if; W[a]:=1; Append(~V, a); end for; print V; // Klaus Brockhaus, Jul 30 2009

Crossrefs

Cf. A118783.

Sequence in context: A355269 A274698 A139790 * A193889 A177922 A102246

Adjacent sequences: A118781 A118782 A118783 * A118785 A118786 A118787

Keyword

nonn

Author

Leroy Quet, Apr 29 2006

Extensions

Extended by Klaus Brockhaus, Jul 30 2009

Status

approved