A172980 a(1)=1, a(2)=3; for n>=3, a(n) is the smallest number larger than a(n-1) such that, for every k<n, a(n) is relatively prime to a(k) iff n is relatively prime to k.

1, 3, 4, 9, 11, 12, 13, 15, 16, 33, 37, 42, 43, 117, 154, 159, 163, 168, 173, 231, 338, 555, 557, 558, 649, 1161, 1168, 1209, 1213, 1254, 1259, 1263, 1406, 1467, 1573, 1578, 1579, 2595, 2752, 2805, 2813, 2964, 2969, 2997, 3014, 5013, 5021, 5022, 5057, 5115

Offset

1,2

Comments

Using the Chinese remainder theorem, it is easy to prove that the sequence is infinite.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..500

Maple

a:= proc(n) option remember;
     local ok, m, k;
     if n<3 then 2*n-1
   else for m from a(n-1)+1 do
          ok:= true;
          for k from 1 to n-1 do
            if igcd(n, k)=1 xor igcd(m, a(k))=1
               then ok:= false; break fi
          od;
          if ok then break fi
        od; m
     fi
    end:
seq (a(n), n=1..50);  # Alois P. Heinz, Nov 21 2010

Mathematica

a[1]=1; a[2]=3; a[n_] := a[n] = For[k = a[n-1]+1, True, k++, If[AllTrue[ Range[n-1], CoprimeQ[k, a[#]] == CoprimeQ[n, #]&], Return[k]]]; Table[ a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 25 2017 *)

Crossrefs

Cf. A151976, A159559, A159560, A159615, A159619, A159629, A159698, A160217.

Sequence in context: A327282 A126269 A319618 * A336930 A035252 A227939

Adjacent sequences: A172977 A172978 A172979 * A172981 A172982 A172983

Keyword

nonn

Author

Vladimir Shevelev, Nov 21 2010

Extensions

More terms from Alois P. Heinz, Nov 21 2010

Status

approved