A110389 Integers with mutual residues -1.

2, 3, 5, 29, 869, 756029, 571580604869, 326704387862983487112029, 106735757048926752040856495274871386126283608869, 11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068029

Offset: 1

Author

Seppo Mustonen, Sep 11 2005

Keywords

• nonn

Comments

This is the special case k=1 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.

Same as A005267 but with the first two terms in reverse order.

Links

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

Crossrefs

Cf. A000289.

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(1,n),n=1..10);

Mathematica

Join[{2,3},NestList[#^2+#-1&,5,10]] (* Harvey P. Dale, Jul 13 2015 *)

Formula

a(1)=2, a(2)=3, a(n) = -1 + a(1)*a(2)*...*a(n-1);

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

Extensions

One more term (a(10)) from Harvey P. Dale, Jul 13 2015