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 A074953 #23 Mar 01 2025 17:37:48
%S A074953 5,9,15,24,36,51,66,87,105,123,144,165,186,195,213,234,255,276,297,
%T A074953 330,384,426,447,492,546,585,609,630,651,735,816,825,843,870,951,1026,
%U A074953 1041,1056,1077,1122,1191,1254,1284,1296,1311,1374,1440
%N A074953 Numbers equidistant from consecutive twin prime pairs.
%H A074953 Amiram Eldar, <a href="/A074953/b074953.txt">Table of n, a(n) for n = 1..10000</a>
%F A074953 a(n) = (A006512(n+1) + A001359(n))/2. - _Michel Marcus_, Jul 26 2015
%e A074953 The twin prime pairs are (3,5), (5,7), (11,13), (17,19), etc. a(n) is equidistant from the higher prime in the n-th pair and the lower prime in the (n+1)th pair. E.g., a(2) is the mean of 7 and 11, which is 9.
%t A074953 t = Select[ Prime@ Range@ 250, PrimeQ[# + 2] &]; Most@ t + Differences[t]/2 + 1 (* _Robert G. Wilson v_, Jul 26 2015 *)
%t A074953 Mean/@Partition[Rest[Flatten[Select[Partition[Prime[Range[250]],2,1],#[[2]]-#[[1]]==2&]]],2] (* _Harvey P. Dale_, Mar 01 2025 *)
%o A074953 (PARI) lista(nn) = {forprime (p=2, nn, q = nextprime(p+1); if (q==p+2, forprime (pp=q, nn, if (nextprime(pp+1) == pp+2, print1((q+pp)/2, ", "); break;););););} \\ _Michel Marcus_, Jul 26 2015
%Y A074953 Cf. A001359, A006512.
%K A074953 nonn
%O A074953 1,1
%A A074953 _Neil Fernandez_, Oct 05 2002