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