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

1,1

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

Formula

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

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 *)

Crossrefs

Cf. A000040, A006093, A037167, A173706.

Sequence in context: A241008 A335126 A367225 * A239929 A246955 A167907

Adjacent sequences: A173705 A173706 A173707 * A173709 A173710 A173711

Keyword

nonn,easy

Author

Jonathan Vos Post, Nov 25 2010

Extensions

More terms from Alois P. Heinz, Nov 26 2010

Status

approved