A173706 Triangle read by rows, of p*(q-1) for primes p, q with p>q.

3, 5, 10, 7, 14, 28, 11, 22, 44, 66, 13, 26, 52, 78, 130, 17, 34, 68, 102, 170, 204, 19, 38, 76, 114, 190, 228, 304, 23, 46, 92, 138, 230, 276, 368, 414, 29, 58, 116, 174, 290, 348, 464, 522, 638, 31, 62, 124, 186, 310, 372, 496, 558, 682, 868

Offset: 1

Author

Jonathan Vos Post, Nov 25 2010

Keywords

• nonn
• easy
• tabl

Comments

The crossing number of a (p,q) torus knot with p > q => 2 is p*(q-1) [Proposition 10.5.3 in Cromwell]

Examples

			   3;
   5,  10;
   7,  14,  28;
  11,  22,  44,  66;
  13,  26,  52,  78, 130;
  17,  34,  68, 102, 170, 204;
		

References

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

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows

Crossrefs

Cf. A000040, A006093.

Programs

Maple

T:= (i,j)-> ithprime(i) *(ithprime(j)-1): seq (seq (T(n,k), k=1..n-1), n=2..11);

Mathematica

Table[Prime[i]*(Prime[j] - 1), {n, 2, 10}, {k, 1, n - 1}] // Flatten (* G. C. Greubel, Nov 23 2016 *)

Formula

T(i,j) = prime(i) * (prime(j)-1) = A000040(i) * (A000040(j)-1) = A000040(i) * A006093(j).

Extensions

Edited by Alois P. Heinz, Nov 25 2010