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

1,1

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Supersequence of A225195 and A242382.

Cf. A091624.

Sequence in context: A341718 A164895 A046859 * A225195 A084289 A183174

Adjacent sequences: A242377 A242378 A242379 * A242381 A242382 A242383

Keyword

nonn

Author

Antonio Roldán, May 12 2014

Status

approved