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 A344868 #10 Jan 28 2022 17:35:45
%S A344868 17,101,191,227,293,431,461,557,571,757,821,863,1039,1193,1213,1277,
%T A344868 1291,1307,1373,1483,1499,1721,1811,2239,2293,2309,2447,2689,3167,
%U A344868 3181,3547,3617,3701,3881,4243,4441,4703,4723,4871,5651,6079,6101,6133,6829,6907,6997,7523,7853,7879,7949
%N A344868 Primes p that are equal to (prime(k)+2*prime(k+1)+3*prime(k+2))/2 for some k.
%C A344868 Corresponding values of k: 2, 10, 17, 20, 24, 33, 35, 41, 42, 53, 57, 60, 68, 77, 78, 81, 82, 83, 87, 93, 94, 104, 109, 131, 134, 135, 140, 153, 176, 177, 193, 196, 201, 209, 222, 233, 246, 247, 256, 288, 306, 307, 308, 337, 341, 344, 367, 379, 380, 382, 393, 395.
%H A344868 Harvey P. Dale, <a href="/A344868/b344868.txt">Table of n, a(n) for n = 1..1000</a>
%e A344868 17 = (3 + 2*5 + 3*7)/2, 101 = (29 + 2*31 + 3*37)/2.
%t A344868 s = {}; Do[If[PrimeQ[p = (Prime[k] + 2*Prime[k + 1] + 3*Prime[k + 2])/2], AppendTo[s, p]], {k, 400}]; s
%t A344868 Select[(#[[1]]+2#[[2]]+3#[[3]])/2&/@Partition[Prime[ Range[ 500]],3,1],PrimeQ] (* _Harvey P. Dale_, Jan 28 2022 *)
%o A344868 (PARI) {p = 3; q = 5; r = 7; for (k = 1, 400, if (isprime (P = (p + 2*q + 3*r)/2), print1 (P ", ")); p = q; q = r; r = nextprime (r + 2))}
%Y A344868 Cf. A034962.
%K A344868 nonn
%O A344868 1,1
%A A344868 _Zak Seidov_, May 31 2021