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 A080188 #10 Feb 08 2020 04:07:00
%S A080188 23,311,349,857,1091,1871,1949,2027,2339,2729,3119,3821,5849,6551,
%T A080188 7487,9437,10139,10529,11699,15287,18251,21059,21839,38609,42899,
%U A080188 49919,51479,57329,61151,65519,69497,70199,70979,81899,97499,108107,109199,114659
%N A080188 Primes p such that 13 is the largest of all prime factors of the numbers between p and the next prime (cf. A052248).
%C A080188 The sequence appears to consist of 23, 349 and the lesser of twin primes q (A001359) such that q+1 is 13-smooth (A080197) but not 11-smooth (A051038, A080196).
%H A080188 Amiram Eldar, <a href="/A080188/b080188.txt">Table of n, a(n) for n = 1..1092</a> (terms below 10^11)
%e A080188 349 is a term since 350 = 2*5^2*7, 351 = 3^3*13, 352 = 2^5*11 are the numbers between 349 and the next prime 353; 857 is a term since 858 = 2*3*11*13 is the only number between 857 and the next prime 859.
%t A080188 maxPrime[n1_, n2_] := FactorInteger[#][[-1, 1]] & /@ Range[n1, n2]; Select[Range[120000], PrimeQ[#] && Max[maxPrime[# + 1, NextPrime[#] - 1]] == 13 &] (* _Amiram Eldar_, Feb 08 2020 *)
%o A080188 (PARI) {forprime(p=2,120000,q=nextprime(p+1); m=0; j=p+1; while(j<q&&m<=13,f=factor(j); a=f[matsize(f)[1],1]; if(m<a,m=a); j++); if(m==13,print1(p,",")))}
%Y A080188 Cf. A052248, A001359, A080197, A051038, A080196.
%K A080188 nonn
%O A080188 1,1
%A A080188 _Klaus Brockhaus_, Feb 10 2003