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A109022 Integers with mutual residues of 2 or more.

%I A109022 #10 Oct 05 2022 04:57:47
%S A109022 3,5,8,14,23,38,44,53,59,62,68,74,83,122,134,143,158,164,173,179,188,
%T A109022 194,203,218,227,242,263,278,284,293,302,314,338,362,374,383,398,404,
%U A109022 422,428,443,452,458,467,479,482,503,509,524,539,542,548,554,563,578
%N A109022 Integers with mutual residues of 2 or more.
%C A109022 This is the special case k=2 of sequences with mutual k-residues. In general, a(1)=k+1 and a(n)=min{m | m>a(n-1), mod(m,a(i))>=k, i=1,...,n-1}. k=0 gives natural numbers A000027 and k=1 prime numbers A000040.
%H A109022 Seppo Mustonen, <a href="http://www.survo.fi/papers/resseq.pdf">On integer sequences with mutual k-residues</a>
%H A109022 Seppo Mustonen, <a href="/A000215/a000215.pdf">On integer sequences with mutual k-residues</a> [Local copy]
%e A109022 The fourth term is 14 since mod(9,3)=0, mod(10,3)=1, mod(11,5)=1,
%e A109022 mod(12,3)=0, mod(13,3)=1 but mod(14,3)=2, mod(14,5)=4, mod(14,8)=6.
%p A109022 res_seq:=proc(a::array(1,nonnegint),k,n::nonnegint) local i,j,m,f; a[1]:=k+1; for i from 2 to n do m:=a[i-1]+1; f:=1; while f=1 do j:=1; while j<i and irem(m,a[j])>=k do j:=j+1; od; if j=i then a[i]:=m; f:=0; else m:=m+1; fi; od; od; end; a:=array(1..57,[]); res_seq(a,2,57); print(a);
%t A109022 seq[k_, n_] := Module[{a, i, j, m, f}, a = Table[0, {n}]; a[[1]] = k+1; For[i = 2, i <= n, i++, m = a[[i-1]]+1; f = 1; While[f == 1, j = 1; While[j < i && Mod[m, a[[j]]] >= k, j = j+1]; If[j == i, a[[i]] = m; f = 0, m = m+1]]]; a];
%t A109022 seq[2, 57] (* _Jean-François Alcover_, Oct 05 2022, after Maple code *)
%Y A109022 Cf. A109328-A109335.
%K A109022 nonn
%O A109022 1,1
%A A109022 _Seppo Mustonen_, Aug 18 2005