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%I #10 Mar 07 2023 03:06:00
%S 3,7,19,139,859,8179,173059,1026199,1827139,15828679,13187242759,
%T 18732483199,912492556939
%N Slowest growing sequence of primes having the prime-pairwise-average property: if i<j, (a(i)+a(j))/2 is prime.
%C Assuming the prime k-tuples conjecture, Granville shows (in section 2.4) that this sequence is infinite.
%H Andrew Granville, <a href="http://www.dms.umontreal.ca/~andrew/PDF/PrimePatterns.pdf">Prime number patterns</a>
%F a(n) = 2*A119751(n)+1. - _Don Reble_, Aug 17 2021
%e The pairwise averages of {3,7,19} are the primes {5,11,13}.
%t s={3, 7}; i=5; Do[While[ !And@@PrimeQ[(s+Prime[i])/2], i++ ]; AppendTo[s, Prime[i]]; i++, {n, 3, 10}]; s
%Y Cf. A113832, A115760, A119751.
%K nonn,hard,more
%O 1,1
%A _T. D. Noe_, Jan 26 2006
%E More terms from _Don Reble_ and _Giovanni Resta_, Feb 15 2006
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