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URL: https://oeis.org/A220533

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A220533
a(n) is minimal number such that the set of all composite numbers <= a(n) contains complete residue system modulo n.
1
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
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Feb 20 2013
EXTENSIONS
Corrected and extended by R. J. Mathar, Feb 27 2013
STATUS
approved