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 A383652 #22 May 13 2025 15:09:23
%S A383652 17,19,41,43,59,61,71,73,101,103,107,109,137,139,149,151,163,167,179,
%T A383652 181,191,193,197,199,227,229,233,239,241,269,271,277,281,283,311,313,
%U A383652 347,349,353,379,383,397,401,419,421,431,433,439,443,457,461,463,487,491,499,503,521,523,563,569,571,593,599
%N A383652 Primes p preceded and followed by gaps whose product is less than (log(p))^2.
%C A383652 Since the geometric mean is never greater than the arithmetic mean: A381850 is a subsequence.
%F A383652 Conjecture: Limit_{n->oo} n / PrimePi(a(n)) = 0.720268...
%e A383652 17 is a term because (17-13)*(19-17)=8 is less than (log(17))^2=8.0271.
%e A383652 19 is a term because (19-17)*(23-19)=8 is less than (log(19))^2=8.6697.
%e A383652 29 is not a term because(29-23)*(31-29)=12 is greater than (log(29))^2=11.3387.
%t A383652 Select[Range[2, 110] // Prime, (# - NextPrime[#, -1])(NextPrime[#] - #) < Log[#]^2 &] (* _Stefano Spezia_, May 04 2025 *)
%o A383652 (PARI) forprime(P=3, 600, my(M=P-precprime(P-1), Q=nextprime(P+1)-P, AR=M*Q, AR0=(log(P))^2); if(AR<AR0, print1(P,", ")));
%Y A383652 A288907 and A381850 are subsequences.
%Y A383652 Cf. A083550.
%K A383652 nonn
%O A383652 1,1
%A A383652 _Alain Rocchelli_, May 04 2025