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

%I A173708 #17 Nov 11 2020 08:24:25
%S A173708 3,5,7,10,11,13,14,17,19,22,23,26,28,29,31,34,37,38,41,43,44,46,47,52,
%T A173708 53,58,59,61,62,66,67,68,71,73,74,76,78,79,82,83,86,89,92,94,97,101,
%U A173708 102,103,106,107,109,113,114,116,118,122,124,127,130,131
%N A173708 Numbers of the form p*(q-1) for primes p, q with p>q.
%C A173708 Sorted A173706. Possible values from the formula for crossing numbers of (p,q) torus knots.
%D A173708 Peter R. Cromwell, Knots and Links, Cambridge University Press, November 15, 2004, p.255.
%H A173708 Alois P. Heinz, <a href="/A173708/b173708.txt">Table of n, a(n) for n = 1..1000</a>
%F A173708 {p*(q-1) : p, q prime and p>q}.
%p A173708 a:= proc(n) option remember;
%p A173708       local k, p, q;
%p A173708       if n=1 then 3
%p A173708       else for k from a(n-1)+1 do
%p A173708              for p in numtheory[factorset](k) do
%p A173708                q:= k/p+1;
%p A173708                if isprime (q) and p>q then return k fi
%p A173708              od
%p A173708            od
%p A173708       fi
%p A173708     end:
%p A173708 seq (a(n), n=1..60);  # _Alois P. Heinz_, Nov 26 2010
%t A173708 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 *)
%Y A173708 Cf. A000040, A006093, A037167, A173706.
%K A173708 nonn,easy
%O A173708 1,1
%A A173708 _Jonathan Vos Post_, Nov 25 2010
%E A173708 More terms from _Alois P. Heinz_, Nov 26 2010