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%I #17 Jul 04 2022 04:38:48
%S 61,1723,4093,17573,21943,46649,110587,195103,287491,314423,405221,
%T 474547,1061189,1191013,1404919,1601609,1906621,2000371,2146687,
%U 2196979,3241783,3511799,4912991,5268017,6229501,6751267,6858997,7077883,11239421,20346407,21951997,26198063
%N Lesser of consecutive primes whose average is a perfect cube.
%H Amiram Eldar, <a href="/A242382/b242382.txt">Table of n, a(n) for n = 1..128</a>
%e 1723 is in the sequence because it is prime, nextprime(1723) = 1733, and average(1723,1733) = 1728 = 12^3.
%t Select[Partition[Prime[Range[2, 10^5]], 2, 1], IntegerQ[Surd[(First[#] + Last[#])/2, 3]] &][[;; , 1]] (* _Amiram Eldar_, Jul 04 2022 *)
%o (PARI) {for(i=3,3*10^7,if(isprime(i),k=(i+nextprime(i+1))/2;if(ispower(k,3),print1(i,", "))))}
%Y Subsequence of A077037 and A242380.
%Y Cf. A225195, A091624.
%K nonn
%O 1,1
%A _Antonio Roldán_, May 12 2014