A334295 Integers k such that the sum of k twin primes pairs starting from (5,7) is a perfect power.

2, 5, 9, 352, 165421, 356928514, 795471483

Offset: 1

Author

Devansh Singh, Apr 21 2020

Keywords

• nonn
• more

Examples

			a(1) = 2 as 5+7 + 11+13 = 36 = 6^2;
a(2) = 5 as 5+7 + 11+13 + 17+19 + 29+31 + 41+43 = 216 = 6^3.
From _Michel Marcus_, Apr 27 2020: (Start)
Table of results, with k, greatest prime and corresponding sum:
   2, 13, 36 = 6^2;
   5, 43, 216 = 6^3;
   9, 109, 900 = 30^2;
   352, 20749, 6290064 = 2508^2;
   165421, 32841799, 5048685437184 = 2246928^2. (End)
From _Giovanni Resta_, Apr 27 2020: (Start)
The next two entries of the table above are:
   356928514, 165800305423, 56622416174760209796 = 7524786786^2;
   795471483, 396030375733, 301922786495024336196 = 17375925486^2. (End)
		

Crossrefs

Cf. A001097 (twin primes), A054735 (sum of twin prime pairs).

Programs

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

Extensions

a(4)-a(5) from Michel Marcus, Apr 22 2020

a(6) from Jinyuan Wang, Apr 24 2020

a(7) from Giovanni Resta, Apr 27 2020