A330978 a(n) = (p1 + p2)/36 such that p1 >= 5 and p2 = p1 + 2 are twin primes and p1 + p2 is a k-th power with k > 1.

1, 4, 6, 49, 64, 144, 196, 225, 841, 1156, 1936, 2601, 3844, 4624, 5776, 6241, 7776, 8281, 9801, 10000, 11449, 15625, 20164, 21609, 24336, 26244, 26569, 29929, 36100, 40804, 44944, 53361, 60025, 63504, 64009, 69696, 87025, 93636, 100489, 108900, 109561, 126025

Offset: 1

Author

Hugo Pfoertner, Jan 05 2020

Keywords

• nonn

Examples

			a(1) = 1: p1 = 17 and p2 = 19 are the first such pair, with p1 + p2 = 36 = 6^2, (17 + 19)/36 = 1;
a(2) = 4: p1 = 71, p2 = 73; p1 + p2 = 144 = 12^2, (71 + 73)/36 = 4.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A119768, A270231, A330980.

Programs

Maple

isa := n -> isprime(n) and isprime(n+2) and iperfpow(2*n+2) <> FAIL:
select(isa, [$4..1000000]): map(n -> (n+1)/18, %); # Peter Luschny, Jan 05 2020

PARI

my(pp=5); forprime(p=7,130000, if(p-pp==2, if(ispower(p+pp), print1((p+pp)/36,", "))); pp=p)