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

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

Author

Vladimir Shevelev, Nov 21 2010

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)

Extensions

More terms from Alois P. Heinz, Nov 21 2010