A173708 Numbers of the form p*(q-1) for primes p, q with p>q.

3, 5, 7, 10, 11, 13, 14, 17, 19, 22, 23, 26, 28, 29, 31, 34, 37, 38, 41, 43, 44, 46, 47, 52, 53, 58, 59, 61, 62, 66, 67, 68, 71, 73, 74, 76, 78, 79, 82, 83, 86, 89, 92, 94, 97, 101, 102, 103, 106, 107, 109, 113, 114, 116, 118, 122, 124, 127, 130, 131

Offset: 1

Author

Jonathan Vos Post, Nov 25 2010

Keywords

• nonn
• easy

Comments

Sorted A173706. Possible values from the formula for crossing numbers of (p,q) torus knots.

References

• Peter R. Cromwell, Knots and Links, Cambridge University Press, November 15, 2004, p.255.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A006093, A037167, A173706.

Programs

Maple

a:= proc(n) option remember;
      local k, p, q;
      if n=1 then 3
      else for k from a(n-1)+1 do
             for p in numtheory[factorset](k) do
               q:= k/p+1;
               if isprime (q) and p>q then return k fi
             od
           od
      fi
    end:
seq (a(n), n=1..60);  # Alois P. Heinz, Nov 26 2010

Mathematica

Reap[For[k = 1, k <= 200, k++, s = Solve[p > q && k == p(q-1), {p, q}, Primes]; If[s != {}, Print[{k, p, q} /. s // First]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, Nov 11 2020 *)

Formula

{p*(q-1) : p, q prime and p>q}.

Extensions

More terms from Alois P. Heinz, Nov 26 2010