OFFSET
1,1
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..128
EXAMPLE
1723 is in the sequence because it is prime, nextprime(1723) = 1733, and average(1723,1733) = 1728 = 12^3.
MATHEMATICA
Select[Partition[Prime[Range[2, 10^5]], 2, 1], IntegerQ[Surd[(First[#] + Last[#])/2, 3]] &][[;; , 1]] (* Amiram Eldar, Jul 04 2022 *)
PROG
(PARI) {for(i=3, 3*10^7, if(isprime(i), k=(i+nextprime(i+1))/2; if(ispower(k, 3), print1(i, ", "))))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Antonio Roldán, May 12 2014
STATUS
approved