A242382 Lesser of consecutive primes whose average is a perfect cube.

61, 1723, 4093, 17573, 21943, 46649, 110587, 195103, 287491, 314423, 405221, 474547, 1061189, 1191013, 1404919, 1601609, 1906621, 2000371, 2146687, 2196979, 3241783, 3511799, 4912991, 5268017, 6229501, 6751267, 6858997, 7077883, 11239421, 20346407, 21951997, 26198063

Offset: 1

Author

Antonio Roldán, May 12 2014

Keywords

• nonn

Examples

			1723 is in the sequence because it is prime, nextprime(1723) = 1733, and average(1723,1733) = 1728 = 12^3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..128

Crossrefs

Subsequence of A077037 and A242380.

Cf. A225195, A091624.

Programs

Mathematica

Select[Partition[Prime[Range[2, 10^5]], 2, 1], IntegerQ[Surd[(First[#] + Last[#])/2, 3]] &][[;; , 1]] (* Amiram Eldar, Jul 04 2022 *)

PARI

{for(i=3,3*10^7,if(isprime(i),k=(i+nextprime(i+1))/2;if(ispower(k,3),print1(i,", "))))}