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 A326392 #20 Sep 11 2019 17:59:30
%S A326392 3,5,11,29,59,179,239,419,1319,3119,3359,7559,21839,35279,42839,55439,
%T A326392 110879,415799,1713599,1867319,1912679,1940399,2489759,3991679,
%U A326392 6652799,6846839,11531519,28828799,85765679,232792559,845404559,1470268799,6285399119,6299092799
%N A326392 Lesser of twin primes p for which sigma(p+1)/sigma(p) reaches record value, where sigma(n) is the divisor sum function (A000203).
%C A326392 Garcia et al. proved that assuming Dickson's conjecture, {sigma(p+1)/sigma(p) : p and p+2 are prime} is dense in [2, oo), and thus this sequence is infinite.
%H A326392 Stephan Ramon Garcia, Florian Luca, Kye Shi, Gabe Udell, <a href="https://arxiv.org/abs/1906.05927">Primitive root bias for twin primes II: Schinzel-type theorems for totient quotients and the sum-of-divisors function</a>, arXiv:1906.05927 [math.NT], 2019.
%H A326392 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dickson%27s_conjecture">Dickson's conjecture</a>.
%e A326392 The values of sigma(p+1)/sigma(p) for the first terms are 1.75 < 2 < 2.333 < 2.4 < 2.8 < ...
%t A326392 s = {}; rm = 0; p = 2; Do[q = NextPrime[p]; If[q - p != 2, p = q; Continue[]]; r = DivisorSigma[1, p + 1]/DivisorSigma[1, p]; If[r > rm, rm = r; AppendTo[s, p]]; p = q, {10^3}]; s
%Y A326392 Cf. A000203, A001359, A006512, A008333.
%K A326392 nonn
%O A326392 1,1
%A A326392 _Amiram Eldar_, Sep 11 2019