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%I #38 Apr 27 2020 09:47:16
%S 2,5,9,352,165421,356928514,795471483
%N Integers k such that the sum of k twin primes pairs starting from (5,7) is a perfect power.
%e a(1) = 2 as 5+7 + 11+13 = 36 = 6^2;
%e a(2) = 5 as 5+7 + 11+13 + 17+19 + 29+31 + 41+43 = 216 = 6^3.
%e From _Michel Marcus_, Apr 27 2020: (Start)
%e Table of results, with k, greatest prime and corresponding sum:
%e 2, 13, 36 = 6^2;
%e 5, 43, 216 = 6^3;
%e 9, 109, 900 = 30^2;
%e 352, 20749, 6290064 = 2508^2;
%e 165421, 32841799, 5048685437184 = 2246928^2. (End)
%e From _Giovanni Resta_, Apr 27 2020: (Start)
%e The next two entries of the table above are:
%e 356928514, 165800305423, 56622416174760209796 = 7524786786^2;
%e 795471483, 396030375733, 301922786495024336196 = 17375925486^2. (End)
%o (PARI) lista(nn) = {my(s = 0, nb = 0); forprime(p=5, nn, if (isprime(p+2), s += 2*p+2; nb++; if (ispower(s), print1(nb, ", "));););} \\ _Michel Marcus_, Apr 22 2020
%Y Cf. A001097 (twin primes), A054735 (sum of twin prime pairs).
%K nonn,more
%O 1,1
%A _Devansh Singh_, Apr 21 2020
%E a(4)-a(5) from _Michel Marcus_, Apr 22 2020
%E a(6) from _Jinyuan Wang_, Apr 24 2020
%E a(7) from _Giovanni Resta_, Apr 27 2020