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 A140111 #4 Mar 14 2021 18:30:02
%S A140111 7,11,23,59,83,97,109,149,233,283,317,337,349,359,367,383,479,487,563,
%T A140111 571,593,641,709,769,823,839,863,1009,1117,1129,1217,1283,1297,1319,
%U A140111 1423,1553,1579,1619,1627,1663,1733,1913,2029,2039,2063,2069,2083,2099,2129
%N A140111 Primes of the form prime(x) + prime(x+1) - (prime(x+1) - prime(x))/2.
%H A140111 Harvey P. Dale, <a href="/A140111/b140111.txt">Table of n, a(n) for n = 1..1000</a>
%e A140111 3+5-(5-3)/2=3+5-1=7, 5+7-(7-5)/2=5+7-1=11, ...
%t A140111 a = {}; Do[p1 = Prime[n]; p2 = Prime[n + 1]; p = p1 + p2 - (p2 - p1)/2; If[PrimeQ[p], AppendTo[a, p]], {n, 10^2}]; a
%t A140111 Select[#[[1]]+#[[2]]-(#[[2]]-#[[1]])/2&/@Partition[ Prime[ Range[ 200]],2,1],PrimeQ] (* _Harvey P. Dale_, Mar 14 2021 *)
%Y A140111 Cf. A092217.
%K A140111 nonn
%O A140111 1,1
%A A140111 _Vladimir Joseph Stephan Orlovsky_, Jun 21 2008
%E A140111 More terms from _Harvey P. Dale_, Mar 14 2021