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 A383216 #19 May 10 2025 03:07:50
%S A383216 113,127,523,887,907,1087,1129,1151,1277,1327,1361,1669,1693,1931,
%T A383216 1951,1973,2203,2311,2333,2477,2557,2971,2999,3163,3251,3299,3469,
%U A383216 4049,4297,4327,4523,4547,4783,4861,5119,5147,5237,5351,5381,5531,5557,5591,5749,5779,5981
%N A383216 Primes p which are preceded and followed by gaps whose difference is greater than 2*log(p).
%C A383216 Primes prime(k) such that abs(prime(k-1)-2*prime(k)+prime(k+1)) > 2*log(prime(k)), where log is the natural logarithm.
%F A383216 Limit_{n->oo} n / PrimePi(a(n)) = 1/e^2 (A092553).
%e A383216 113 is a term because abs(109-2*113+127)=12 and 2*log(113)=9.4548.
%e A383216 127 is a term because abs(113-2*127+131)=10 and 2*log(127)=9.6884.
%t A383216 Select[Prime[Range[2,782]],Abs[NextPrime[#,-1]-2#+NextPrime[#]]>2Log[#]&] (* _James C. McMahon_, Apr 27 2025 *)
%o A383216 (PARI) forprime(P=3, 6000, my(M=P-precprime(P-1), Q=nextprime(P+1)-P, AR1=min(M,Q), AR2=max(M,Q), AR0=2*log(P)); if(AR2-AR1>AR0, print1(P,", ")));
%Y A383216 Cf. A036263, A383215, A092553.
%K A383216 nonn
%O A383216 1,1
%A A383216 _Alain Rocchelli_, Apr 19 2025