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A138755 Primes p2 such that p1^3 + p2^2 is an average of twin primes and p1 < p2 are consecutive primes.

%I A138755 #16 Sep 08 2022 08:45:33
%S A138755 29,2081,2357,3373,3727,4013,4093,5233,6007,7829,15559,15797,16319,
%T A138755 17123,18523,20143,22037,23071,25261,26293,28019,28289,33797,39499,
%U A138755 41627,42181,42929,45121,48533,48823,49123,50417,52697,54629,57973,58897,60887,62761,64381
%N A138755 Primes p2 such that p1^3 + p2^2 is an average of twin primes and p1 < p2 are consecutive primes.
%H A138755 Amiram Eldar, <a href="/A138755/b138755.txt">Table of n, a(n) for n = 1..10000</a>
%e A138755 29 is a term since 23 and 29 are consecutive primes, 23^3 + 29^2 = 13008, and (13007, 13009) are twin primes.
%t A138755 a={};Do[p1=Prime[n];p2=Prime[n+1];pp=p1^3+p2^2;If[PrimeQ[pp-1]&&PrimeQ[pp+1],AppendTo[a,p2]],{n,16^3}];Print[a];
%t A138755 Select[Partition[Prime[Range[6500]],2,1],AllTrue[#[[1]]^3+#[[2]]^2+{1,-1},PrimeQ]&][[All,2]] (* _Harvey P. Dale_, Aug 29 2021 *)
%o A138755 (Magma) [NthPrime(k+1):k in [1..7000]| IsPrime(q-1) and IsPrime(q+1) where q is NthPrime(k)^3+ NthPrime(k+1)^2]; // _Marius A. Burtea_, Dec 22 2019
%Y A138755 Cf. A001097, A001359, A006512, A014574.
%Y A138755 Cf. A138716, A139777, A139780.
%K A138755 nonn
%O A138755 1,1
%A A138755 _Vladimir Joseph Stephan Orlovsky_, May 15 2008
%E A138755 More terms from _Amiram Eldar_, Dec 22 2019