A220533 a(n) is minimal number such that the set of all composite numbers <= a(n) contains complete residue system modulo n.

4, 9, 8, 15, 12, 35, 14, 27, 20, 33, 24, 65, 26, 45, 32, 45, 36, 77, 38, 63, 44, 63, 46, 95, 48, 69, 56, 87, 60, 187, 62, 93, 64, 105, 72, 175, 74, 117, 80, 123, 84, 215, 86, 117, 92, 135, 94, 245, 96, 153, 104, 141, 106, 245, 108, 165, 116

Offset: 1

Author

Vladimir Shevelev, Feb 20 2013

Keywords

• nonn

Crossrefs

Cf. A038026, A210537, A211204.

Programs

Maple

A220533 := proc(n)
    local sco,c,ai,scor ;
    sco := {} ;
    for ai from 1 do
        sco := sco union {A002808(ai)} ;
        scor := convert( [seq(c mod n,c=sco)], set) ;
        if nops(scor) = n then
            return A002808(ai) ;
        end if;
    end do:
end proc:
seq(A220533(n),n=1..60) ; # R. J. Mathar, Feb 27 2013

Mathematica

A002808[n_] := A002808[n] = Module[{a}, If[ n == 1 , 4, For[a = A002808[n-1] + 1 , True, a++, If[! PrimeQ[a], Return [a]]]]]; A220533[n_] := Module[{ sco, c, ai, scor}, sco = {}; For[ai = 1, True, ai++, AppendTo[sco, A002808[ai]] ; scor = Mod[#, n]& /@ sco // Union; If[Length[scor] == n , Return[A002808[ai]]]]]; Table[A220533[n], {n, 1, 57}] (* Jean-François Alcover, Feb 28 2013, translated from R. J. Mathar's Maple program *)

Formula

For odd n, a(n) <= 2n + 2; the equality holds if and only if n + 2 is prime.

a(n)<2*n for 25,33,49,... - R. J. Mathar and Vladimir Shevelev, Feb 28 2013

Extensions

Corrected and extended by R. J. Mathar, Feb 27 2013