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 A113875 #14 Jun 27 2024 01:32:09
%S A113875 3,7,19,139,859,8179,173059,1026199,1827139,15828679,13187242759,
%T A113875 18732483199,912492556939,9130567625119
%N A113875 Slowest growing sequence of primes having the prime-pairwise-average property: if i<j, (a(i)+a(j))/2 is prime.
%C A113875 Assuming the prime k-tuples conjecture, Granville shows (in section 2.4) that this sequence is infinite.
%H A113875 Andrew Granville, <a href="https://doi.org/10.1080/00029890.2008.11920529">Prime number patterns</a>, The American Mathematical Monthly, Vol. 115, No. 4 (2008), pp. 279-296; <a href="https://dms.umontreal.ca/~andrew/PDF/PrimePatterns.pdf">alternative link</a>.
%F A113875 a(n) = 2*A119751(n)+1. - _Don Reble_, Aug 17 2021
%e A113875 The pairwise averages of {3,7,19} are the primes {5,11,13}.
%t A113875 s={3, 7}; i=5; Do[While[ !And@@PrimeQ[(s+Prime[i])/2], i++ ]; AppendTo[s, Prime[i]]; i++, {n, 3, 10}]; s
%Y A113875 Cf. A113832, A115760, A119751.
%K A113875 nonn,hard,more
%O A113875 1,1
%A A113875 _T. D. Noe_, Jan 26 2006
%E A113875 More terms from _Don Reble_ and _Giovanni Resta_, Feb 15 2006
%E A113875 a(14) from _Amiram Eldar_, Jun 27 2024