A173381 a(n) = b_n(p_(n+1)) where p_n is the n-th prime, b_n(1)=1, b_n(2)=p_n, and for k>=3, b_n(k) is the smallest number larger than b_n(k-1) such that, for all i<k, b_n(k) is relatively prime to b_n(i) iff k is relatively prime to i.

3, 11, 31, 163, 661, 929, 2041, 21341, 15989, 47387, 125117, 263411, 123493, 10426601, 3654221, 4167127, 86622397, 4036267, 3910993, 541513877

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Maple

b:= proc(n, k) option remember; local ok, m, i;
      if k=1 then 1
    elif k=2 then ithprime(n)
    else for m from b(n, k-1)+1 do
           ok:= true;
           for i from 1 to k-1 do
             if igcd(k, i)=1 xor igcd(m, b(n, i))=1
                then ok:= false; break fi
           od;
           if ok then break fi
         od; m
      fi
    end:
a:= n-> b(n, ithprime(n+1));
seq(a(n), n=1..10);  # Alois P. Heinz, Nov 22 2010

Mathematica

b[n_, k_] := b[n, k] = Module[{ok, m, i}, Which[k==1, 1, k==2, Prime[n], True, For[m = b[n, k - 1] + 1, True, m++, ok = True; For[i = 1, i <= k - 1, i++, If[Xor[GCD[k, i]==1, GCD[m, b[n, i]]==1],  ok = False; Break[]]]; If[ok, Break[]]]; m]];
a[n_] := b[n, Prime[n + 1]];
Array[a, 10] (* Jean-François Alcover, Nov 28 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000040, A172980, A172999.

Sequence in context: A146456 A095692 A163421 * A076477 A319335 A104079

Adjacent sequences: A173378 A173379 A173380 * A173382 A173383 A173384

Keyword

nonn

Author

Vladimir Shevelev, Nov 22 2010

Extensions

More terms from Alois P. Heinz, Nov 22 2010

Status

approved