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 A105173 #13 Jul 18 2021 06:49:36
%S A105173 3,7,8,15,16,23,24,32,39,40,47,48,55,56,63,64,71,79,80,87,95,103,104,
%T A105173 111,112,119,120,128,135,136,143,151,152,159,167,175,176,183,199,208,
%U A105173 216,223,224,231,232,239,240,247,248,255,256,263,264,271,279,287,288
%N A105173 Numbers k such that either k*(k+1)/4 + 1 or k*(k+1)/4 - 1 or both are primes.
%C A105173 The primes are (sum of numbers from 1 to k)/2 + or - 1.
%H A105173 Amiram Eldar, <a href="/A105173/b105173.txt">Table of n, a(n) for n = 1..10000</a>
%e A105173 3*4/4 = 3, 3-1 = 2 is prime so a(1) = 3.
%e A105173 7*8/4 = 14, 14-1 = 13 is prime so a(2) = 7.
%e A105173 8*9/4 = 18, 18-1 = 17 is prime, 18+1 = 19 is prime, so a(3) = 8.
%t A105173 Select[Range[300], Or @@ PrimeQ[#*(#+1)/4 + {-1, 1}] &] (* _Amiram Eldar_, Jul 18 2021 *)
%Y A105173 Subsequence of A014601.
%K A105173 nonn
%O A105173 1,1
%A A105173 _Pierre CAMI_, Apr 11 2005
%E A105173 More terms from _Amiram Eldar_, Jul 18 2021