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 A326356 #25 Feb 12 2021 12:07:52
%S A326356 5,2381,3851,20021,50051,52361,424271,470471,602141,2302301,6806801,
%T A326356 16926911,17497481,69989921,78278201,183953771,242662421,468818351,
%U A326356 2156564411,24912037151,43874931101,73769375681,131104243271,1360122864101,1943064533411,2635321709021,3075260848661,4078063299311
%N A326356 Lesser of twin primes p >= 5 for which phi(p+1)/phi(p-1) reaches record value, where phi(n) is the Euler totient function (A000010).
%C A326356 Terms a(2)-a(23) were taken from the paper by Garcia et al.
%C A326356 Garcia et al. proved that assuming Dickson's conjecture, {phi(p+1)/phi(p-1) : p and p+2 are prime} is dense in [0, oo), and thus this sequence is infinite.
%C A326356 They give an example of a term p with 1099 digits with phi(p+1)/phi(p-1) = 3.11615...
%C A326356 What is the least value of lesser of twin primes p such that phi(p+1)/phi(p-1) > 2?
%C A326356 A candidate is p = 8183287190196092135163947564054981234789530779544672356881 for which the ratio is equal to 2.00047615... . - _Giovanni Resta_, Nov 01 2019
%H A326356 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 A326356 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dickson%27s_conjecture">Dickson's conjecture</a>.
%e A326356 The values of phi(p+1)/phi(p-1) for the first terms are 1 < 1.031... < 1.06 < 1.118... < 1.12 < ...
%t A326356 s = {}; rm = 0; p = 5; Do[q = NextPrime[p]; If[q - p != 2, p = q; Continue[]]; r = EulerPhi[p + 1]/EulerPhi[p - 1]; If[r > rm, rm = r; AppendTo[s, p]]; p = q, {10^6}]; s
%Y A326356 Cf. A000010, A001359, A006512, A008330, A008331, A286714, A303549, A326391.
%Y A326356 Except for 5, subsequence of A286715.
%K A326356 nonn
%O A326356 1,1
%A A326356 _Amiram Eldar_, Sep 11 2019
%E A326356 a(24)-a(28) from _Giovanni Resta_, Nov 01 2019