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Integers with mutual residues -2.
2

%I #20 Mar 05 2019 19:58:23

%S 3,5,13,193,37633,1416317953,2005956546822746113,

%T 4023861667741036022825635656102100993,

%U 16191462721115671781777559070120513664958590125499158514329308740975788033

%N Integers with mutual residues -2.

%C This is the special case k=2 of sequences with mutual residues -k. In general, a(1)=k+1 and a(n)=min{m | m>a(n-1), mod(m,a(i))=-k, i=1,...,n-1}.

%C An infinite coprime sequence

%H S. Mustonen, <a href="http://www.survo.fi/papers/resseq.pdf">On integer sequences with mutual k-residues</a>

%F a(1)=3, a(2)=5, a(n)=-2+a(1)*a(2)*...*a(n-1) [typo corrected by _Vincenzo Librandi_, Feb 08 2010]

%F a(n)=a(n-1)^2+2*a(n-1)-2, for n>3.

%F Apparently a(n)=A003010(n-2)-1 for n>=3. - _R. J. Mathar_, Apr 22 2007

%p a:=proc(k,n::nonnegint) option remember; if n<3 then RETURN(n*k+1); fi; if n=3 then RETURN(a(k,1)*a(k,2)-k); fi; a(k,n-1)*(a(k,n-1)+k)-k; end; seq(a(2,n),n=1..9);

%t Join[{3,5},NestList[#^2+2#-2&,13,6]] (* _Harvey P. Dale_, Mar 05 2019 *)

%K nonn

%O 1,1

%A _Seppo Mustonen_, Sep 11 2005