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

1,1

Links

Table of n, a(n) for n=1..57.

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

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 *)

Crossrefs

Cf. A038026, A210537, A211204.

Sequence in context: A348512 A140808 A163642 * A357313 A085084 A248390

Adjacent sequences: A220530 A220531 A220532 * A220534 A220535 A220536

Keyword

nonn

Author

Vladimir Shevelev, Feb 20 2013

Extensions

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

Status

approved