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 A270696 #14 Jun 22 2022 10:54:13 %S A270696 4,9,64,81,144,225,324,441,625,1089,1681,1728,2601,3600,4096,5184, %T A270696 6084,8464,12544,13689,16641,17576,19044,19600,21952,25281,27225, %U A270696 28224,29584,36864,38025,39204,45369,46656,47524,51984,56169,74529,87025,88804,91809,92416,95481 %N A270696 Perfect powers that are the average of two consecutive primes. %C A270696 The corresponding lesser primes are in A242380. - _Michel Marcus_, Mar 23 2016 %H A270696 Charles R Greathouse IV, <a href="/A270696/b270696.txt">Table of n, a(n) for n = 1..10000</a> %e A270696 1728 is a term because 1728 = 12^3 = (1723 + 1733)/2. %t A270696 Select[Mean/@Partition[Prime[Range[10000]],2,1],GCD@@FactorInteger[#][[All,2]]>1&] (* _Harvey P. Dale_, Jun 22 2022 *) %o A270696 (PARI) for(n=2, 1e5, if((nextprime(n) - n) == (n - precprime(n)) && ispower(n), print1(n, ", "))); %o A270696 (PARI) list(lim)=my(v=List(),t); forprime(e=2,logint(lim\=1,2), for(m=2,sqrtnint(lim,e), t=m^e; if(t-precprime(t)==nextprime(t)-t, listput(v,t)))); Set(v) \\ _Charles R Greathouse IV_, Mar 21 2016 %Y A270696 Cf. A001597, A024675, A242380. %K A270696 nonn %O A270696 1,1 %A A270696 _Altug Alkan_, Mar 21 2016