A034796 a(1)=1, a(n-1) is a square mod a(n), and a(n) > a(n-1).

1, 2, 7, 9, 10, 13, 17, 19, 25, 26, 34, 37, 41, 43, 49, 50, 62, 67, 73, 74, 82, 87, 89, 94, 97, 99, 105, 106, 109, 113, 121, 122, 127, 129, 130, 133, 137, 139, 145, 146, 157, 162, 167, 173, 178, 181, 185, 187, 193, 194, 206, 214, 217, 218, 223, 237, 241, 243, 249

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• nice

Comments

a(n) is the smallest number larger than a(n-1) such that a(n-1) is a quadratic residue mod a(n). - R. J. Mathar, Jul 27 2015

Examples

			For n=3 we have a(2)=2. 2 is not quadratic residue mod 3 because the quadratic residues mod 3 are {0,1}, see A011655. 2 is not a quadratic residue mod 4 because the quadratic residues mod 4 are {0,1}, see A000035. 2 is not a quadratic residue mod 5 because the quadratic residues mod 5 are {0,1,4}, see A070430. 2 is not a quadratic residue mod 6 because the quadratic residues mod 6 are {0,1,3,4}, see A070431. 2 is a quadratic residue mod 7 because the quadratic residues mod 7 are {0,1,2,4}, see A053879. So a(3)=7. - _R. J. Mathar_, Jul 27 2015
		

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Programs

Maple

A034796 := proc(n)
    option remember;
    if n = 1 then
        1;
    else
        for a from procname(n-1)+1 do
            if numtheory[quadres](procname(n-1),a) = 1 then
                return a;
            end if;
        end do:
    end  if;
end proc: # R. J. Mathar, Jul 27 2015

Mathematica

residueQ[n_, k_] := Length[ Select[ Range[ Floor[k/2]]^2, Mod[#, k] == n &, 1]] == 1; a[1] = 1; a[n_] := a[n] = For[k = a[n-1] + 1, True, k++, If[residueQ[a[n-1], k], Return[k]]]; Table[a[n], {n, 1, 60}] (* Jean-François Alcover, Aug 13 2013 *)

Extensions

Clarified definition, Joerg Arndt, Aug 14 2013