A110407 Integers with mutual residues -2.

3, 5, 13, 193, 37633, 1416317953, 2005956546822746113, 4023861667741036022825635656102100993, 16191462721115671781777559070120513664958590125499158514329308740975788033

Offset: 1

Author

Seppo Mustonen, Sep 11 2005

Keywords

• nonn

Comments

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}.

An infinite coprime sequence

Links

• S. Mustonen, On integer sequences with mutual k-residues

Programs

Maple

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);

Mathematica

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

Formula

a(1)=3, a(2)=5, a(n)=-2+a(1)*a(2)*...*a(n-1) [typo corrected by Vincenzo Librandi, Feb 08 2010]

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

Apparently a(n)=A003010(n-2)-1 for n>=3. - R. J. Mathar, Apr 22 2007