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.
%I A244175 #19 Dec 17 2016 11:04:14 %S A244175 6,14,21,26,33,35,51,69,74,87,93,111,119,122,129,143,146,161,185,203, %T A244175 209,215,219,278,287,299,303,305,314,321,341,371,381,395,413,437,458, %U A244175 482,489,515,527,533,537,545,551,591,629,671,698,707,713,717,734,737,755 %N A244175 Semiprimes s = p*q such that (p+q)^2 - s is prime. %C A244175 All terms are squarefree, since primes p and q must be distinct. (Otherwise, we would have (p+q)^2 - s = (2p)^2 - p^2 = 3p^2, which could not be prime.) - _Jon E. Schoenfield_, Dec 16 2016 %H A244175 Alois P. Heinz, <a href="/A244175/b244175.txt">Table of n, a(n) for n = 1..10000</a> %e A244175 The terms 6, 14, 21 and 581543 are in the sequence because: %e A244175 2^2 + 2*3 + 3^2 = (2+3)^2 - 6 = 19 is prime. %e A244175 2^2 + 2*7 + 7^2 = (2+7)^2 - 14 = 67 is prime. %e A244175 3^2 + 3*7 + 7^2 = (3+7)^2 - 21 = 79 is prime. %e A244175 677^2 + 677*859 + 859^2 = (677+859)^2 - 581543 = 1777753 is prime. %t A244175 max = 1000; Reap[For[p=2, p <= Sqrt[max], p = NextPrime[p], For[q=NextPrime[p], p*q <= max, q=NextPrime[q], If[PrimeQ[(p+q)^2-p*q], Sow[p*q]]]]][[2, 1]] // Sort (* _Jean-François Alcover_, Dec 09 2014 *) %t A244175 Select[Select[Range[10^3], SquareFreeQ@ # && PrimeOmega@ # == 2 &], %t A244175 Function[s, PrimeQ[(#1 + #2)^2 - s] & @@ FactorInteger[s][[All, 1]]]] (* _Michael De Vlieger_, Dec 17 2016 *) %Y A244175 Subsequence of A006881. %Y A244175 Cf. A244146. %K A244175 nonn %O A244175 1,1 %A A244175 _Peter Luschny_, Jun 21 2014