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 A184417 #25 Sep 10 2023 21:55:11 %S A184417 33,73,289,649,1801,3529,7201,10369,20809,23329,38089,45001,64801, %T A184417 73729,78409,103969,115201,145801,159049,194689,242209,352801,373249, %U A184417 426889,544969,649801,720001,763849,824329,871201,1312201,1351369,1371169,1472329,1555849,2080801,2130049,2205001,2255689,2384929,2654209 %N A184417 p^2 + (p+2)^2 - 1 where (p,p+2) is the n-th twin prime pair. %C A184417 This seems to have a disproportionately high probability of generating a prime number. %F A184417 a(n) = A063533(n) - 1. %e A184417 a(1) = prime(1)^2 + (prime(1)+2)^2 - 1 = 3^2 + (3+2)^2 - 1 = 33; %e A184417 a(2) = prime(2)^2 + (prime(2)+2)^2 - 1 = 5^2 + (5+2)^2 - 1 = 73; %e A184417 a(3) = prime(3)^2 + (prime(3)+2)^2 - 1 = 11^2 + (11+2)^2 - 1 = 289. %t A184417 Total/@(Select[Partition[Prime[Range[500]],2,1],#[[2]]-#[[1]]==2&]^2)-1 (* _Harvey P. Dale_, Feb 24 2011 *) %K A184417 nonn %O A184417 1,1 %A A184417 _Robert Mohr_, Feb 13 2011