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 A268963 #10 Feb 20 2019 08:05:45
%S A268963 5,13,29,89,137,229,509,1549,1861,9601,15733,16829,33289,39709,50741,
%T A268963 180949,183289,1562053,1638053,2244157,4469141,4874977,7856713,
%U A268963 10087481,12021353,12214273,18227081,148364081,292182557,320262769,468214457,727335397,869766761
%N A268963 Primes 4k+1 at the end of the maximal gaps in A084162.
%C A268963 Subsequence of A002144.
%C A268963 A084161 lists the primes preceding the maximal gaps, and A084162 lists the corresponding gap sizes. See more comments there.
%H A268963 Alexei Kourbatov, <a href="/A268963/b268963.txt">Table of n, a(n) for n = 0..42</a>
%F A268963 a(n) = A084161(n) + A084162(n)
%e A268963 a(3) = 89: There are no primes p = 1 mod 4 between 73 and 89, this gap is the largest up to 89, the gap size is 16.
%t A268963 Reap[Print[5]; Sow[5]; r = 0; p = 5; For[q = 7, q < 10^7, q = NextPrime[q], If[Mod[q, 4] == 3, Continue[]]; g = q - p; If[g > r, r = g; Print[q] Sow[q]]; p = q]][[2, 1]] (* _Jean-François Alcover_, Feb 20 2019, from PARI *)
%o A268963 (PARI) print1(5); r=0; p=5; forprime(q=7, 1e9, if(q%4==3, next); g=q-p; if(g>r, r=g; print1(", "q)); p=q)
%Y A268963 Cf. A002144, A002313, A084161, A084162.
%K A268963 nonn
%O A268963 0,1
%A A268963 _Alexei Kourbatov_, Feb 16 2016