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 A383215 #22 May 10 2025 03:07:55
%S A383215 7,29,31,113,127,139,149,181,191,199,223,241,283,307,317,331,347,419,
%T A383215 421,431,467,521,523,541,619,641,661,673,773,809,811,821,829,853,863,
%U A383215 877,887,907,953,967,1009,1021,1031,1049,1051,1061,1069,1087,1129,1151,1153,1213,1259,1277
%N A383215 Primes p preceded and followed by gaps whose difference (absolute value) is greater than log(p).
%C A383215 Primes prime(k) such that abs(prime(k-1)-2*prime(k)+prime(k+1)) > log(prime(k)), where log is the natural logarithm.
%C A383215 a(n) ~ prime(round(n*e)) as n tends to infinity, where e is Euler's number.
%F A383215 Limit_{n->oo} n / PrimePi(a(n)) = 1/e (A068985).
%e A383215 7 is a term because abs(5-2*7+11)=2 and log(7)=1.9459.
%e A383215 29 is a term because abs(23-2*29+31)=4 and log(29)=3.3673.
%t A383215 Select[Prime[Range[2,206]],Abs[NextPrime[#,-1]-2#+NextPrime[#]]>Log[#]&] (* _James C. McMahon_, Apr 29 2025 *)
%o A383215 (PARI) forprime(P=3, 1300, my(M=P-precprime(P-1), Q=nextprime(P+1)-P, AR1=min(M,Q), AR2=max(M,Q), AR0=log(P)); if(AR2-AR1>AR0, print1(P,", ")));
%Y A383215 Cf. A036263, A383216, A068985.
%K A383215 nonn
%O A383215 1,1
%A A383215 _Alain Rocchelli_, Apr 19 2025