cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

This page as a plain text file.
%I A173706 #18 Nov 24 2016 09:02:49
%S A173706 3,5,10,7,14,28,11,22,44,66,13,26,52,78,130,17,34,68,102,170,204,19,
%T A173706 38,76,114,190,228,304,23,46,92,138,230,276,368,414,29,58,116,174,290,
%U A173706 348,464,522,638,31,62,124,186,310,372,496,558,682,868
%N A173706 Triangle read by rows, of p*(q-1) for primes p, q with p>q.
%C A173706 The crossing number of a (p,q) torus knot with p > q => 2 is p*(q-1) [Proposition 10.5.3 in Cromwell]
%D A173706 Peter R. Cromwell, Knots and Links, Cambridge University Press, November 15, 2004, p. 255.
%H A173706 G. C. Greubel, <a href="/A173706/b173706.txt">Table of n, a(n) for the first 50 rows</a>
%F A173706 T(i,j) = prime(i) * (prime(j)-1) = A000040(i) * (A000040(j)-1) = A000040(i) * A006093(j).
%e A173706    3;
%e A173706    5,  10;
%e A173706    7,  14,  28;
%e A173706   11,  22,  44,  66;
%e A173706   13,  26,  52,  78, 130;
%e A173706   17,  34,  68, 102, 170, 204;
%p A173706 T:= (i,j)-> ithprime(i) *(ithprime(j)-1): seq (seq (T(n,k), k=1..n-1), n=2..11);
%t A173706 Table[Prime[i]*(Prime[j] - 1), {n, 2, 10}, {k, 1, n - 1}] // Flatten (* _G. C. Greubel_, Nov 23 2016 *)
%Y A173706 Cf. A000040, A006093.
%K A173706 nonn,easy,tabl
%O A173706 1,1
%A A173706 _Jonathan Vos Post_, Nov 25 2010
%E A173706 Edited by _Alois P. Heinz_, Nov 25 2010