A242380 Lesser of consecutive primes whose average is a perfect power.

3, 7, 61, 79, 139, 223, 317, 439, 619, 1087, 1669, 1723, 2593, 3593, 4093, 5179, 6079, 8461, 12541, 13687, 16633, 17573, 19037, 19597, 21943, 25261, 27211, 28219, 29581, 36857, 38011, 39199, 45361, 46649, 47521, 51977, 56167, 74527, 87013, 88801, 91807, 92413, 95479

Offset: 1

Author

Antonio Roldán, May 12 2014

Keywords

• nonn

Examples

			4093 is in the sequence because 4093 and 4099 are consecutive primes and (4093 + 4099)/2 = 4096 = 2^12.
		

Links

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

Crossrefs

Supersequence of A225195 and A242382.

Cf. A091624.

Programs

Mathematica

Select[Partition[Prime[Range[2, 10^4]], 2, 1], GCD @@ FactorInteger[(First[#] + Last[#])/2][[;; , 2]] > 1 &][[;; , 1]] (* Amiram Eldar, Jul 04 2022 *)

PARI

for(i=3, 10^5, if(isprime(i), k=(i+nextprime(i+1))/2; if(ispower(k), print1(i, ", "))))