A165744 Numbers k with property that 6^k is the sum of two consecutive primes.

2, 3, 7, 36, 54, 143, 1102, 1678

Offset: 1

Author

Zak Seidov, Sep 26 2009

Keywords

• nonn
• more

Examples

			k=2: 6^2 = 36     = 17 + 19         = prime(7) + prime(8);
k=3: 6^3 = 216    = 107 + 109       = prime(28) + prime(29);
k=7: 6^7 = 279936 = 139967 + 139969 = prime(13005) + prime(13006).
		

Crossrefs

Cf. A071087, A074924.

Programs

Mathematica

(* M6 *) Do[If[PreviousPrime[6^n/2]+NextPrime[6^n/2]==6^n,Print[n]],{n,1000}]

PARI

is(k) = my(t=6^k); precprime(t/2)+nextprime(1+t/2)==t; \\ Jinyuan Wang, Feb 18 2021

Extensions

a(7) from Max Alekseyev, Dec 14 2011

a(8) from Amiram Eldar, Apr 06 2019