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%I #18 Jul 04 2022 04:38:53
%S 3,7,61,79,139,223,317,439,619,1087,1669,1723,2593,3593,4093,5179,
%T 6079,8461,12541,13687,16633,17573,19037,19597,21943,25261,27211,
%U 28219,29581,36857,38011,39199,45361,46649,47521,51977,56167,74527,87013,88801,91807,92413,95479
%N Lesser of consecutive primes whose average is a perfect power.
%H Amiram Eldar, <a href="/A242380/b242380.txt">Table of n, a(n) for n = 1..10000</a>
%e 4093 is in the sequence because 4093 and 4099 are consecutive primes and (4093 + 4099)/2 = 4096 = 2^12.
%t Select[Partition[Prime[Range[2, 10^4]], 2, 1], GCD @@ FactorInteger[(First[#] + Last[#])/2][[;; , 2]] > 1 &][[;; , 1]] (* _Amiram Eldar_, Jul 04 2022 *)
%o (PARI) for(i=3, 10^5, if(isprime(i), k=(i+nextprime(i+1))/2; if(ispower(k), print1(i, ", "))))
%Y Supersequence of A225195 and A242382.
%Y Cf. A091624.
%K nonn
%O 1,1
%A _Antonio Roldán_, May 12 2014