login
A118783
a(1) = 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.
2
1, 2, 4, 3, 8, 5, 12, 9, 13, 11, 19, 15, 23, 21, 20, 25, 32, 18, 35, 24, 30, 29, 43, 28, 41, 37, 44, 38, 55, 27, 60, 47, 49, 51, 56, 42, 71, 54, 61, 50, 79, 46, 83, 63, 65, 68, 91, 59, 87, 67, 81, 75, 104, 66, 93, 77, 88, 85, 115, 57, 119, 96, 90, 99, 109, 73, 131, 102, 105, 80
OFFSET
1,2
LINKS
EXAMPLE
The first 7 terms of the sequence are 1,2,4,3,8,5,12. Of these there are 3 terms that are coprime to 8 (those terms being 1, 3 and 5). So a(8) is the 3rd positive integer missing from the first 7 terms of the sequence (i.e., is the 3rd integer of the sequence 6, 7, 9, 10, 11, 13, ...). So a(8) = 9.
MATHEMATICA
a = {1}; Do[AppendTo[a, Complement[Range[2 Max@a], a][[Length@Select[a, GCD[#, n] == 1 &]]]], {n, 2, 70}]; 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 [2..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. A118784.
Sequence in context: A109812 A137622 A376906 * A242706 A242722 A120242
KEYWORD
nonn
AUTHOR
Leroy Quet, Apr 29 2006
EXTENSIONS
Extended by Klaus Brockhaus, Jul 30 2009
STATUS
approved