A330980 a(n) = (p1 + p2)/216 such that p1 >= 5 and p2 = p1 + 2 are twin primes and p1 + p2 is a k-th power with k >= 3.

1, 1296, 24389, 274625, 531441, 970299, 2343750, 2515456, 4492125, 5268024, 5451776, 6967871, 8000000, 18821096, 25672375, 27270901, 32461759, 37748736, 41421736, 43243551, 50653000, 64000000, 69426531, 80062991, 81746504, 82881856, 94818816, 100663296

Offset: 1

Author

Hugo Pfoertner, Jan 05 2020

Keywords

• nonn

Comments

The values of k corresponding to the first terms are: 3, 7, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 5, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, ...

Examples

			a(1) = 1: p1 = 107 and p2 = 109 is the first pair with a sum that is a 3rd power, 216=6^3;
a(2) = 1296: p1 = 1296*108 - 1 = 139967, p2 = 1296*108 + 1 = 139969, p1 + p2 = 279936 = 6^7.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A076467, A119768, A270231, A330978.

Programs

PARI

my(pp=5,j); forprime(p=7,10000000000, if(p-pp==2, if(j=ispower(p+pp), if(j>2, print1((p+pp)/216,", ")))); pp=p)