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A138716 Primes p2 such that p1^2 + p2^3 is an average of twin primes and p1 < p2 are consecutive primes.

%I A138716 #15 Oct 29 2022 15:58:23
%S A138716 29,107,1481,1613,2393,2879,4421,5021,5519,5573,6269,7817,8447,9629,
%T A138716 11489,11981,12011,17159,17573,18461,19961,21713,23021,23291,23747,
%U A138716 24917,26339,27947,29021,29201,29663,30893,32063,32717,34217,34589,35159,36527,36899,44753
%N A138716 Primes p2 such that p1^2 + p2^3 is an average of twin primes and p1 < p2 are consecutive primes.
%H A138716 Amiram Eldar, <a href="/A138716/b138716.txt">Table of n, a(n) for n = 1..10000</a>
%e A138716 29 is a term since 23 and 29 are consecutive primes, 23^2 + 29^3 = 24918, and (24917, 24919) are twin primes.
%t A138716 a={};Do[p1=Prime[n];p2=Prime[n+1];pp=p1^2+p2^3;If[PrimeQ[pp-1]&&PrimeQ[pp+1],AppendTo[a,p2]],{n,16^3}];Print[a];
%t A138716 Select[Partition[Prime[Range[5000]],2,1],AllTrue[#[[1]]^2+#[[2]]^3+{1,-1},PrimeQ]&] [[All,2]] (* _Harvey P. Dale_, Oct 29 2022 *)
%o A138716 (Magma) [NthPrime(k+1):k in [1..5000]| IsPrime(q-1) and IsPrime(q+1) where q is NthPrime(k)^2+ NthPrime(k+1)^3]; // _Marius A. Burtea_, Dec 22 2019
%Y A138716 Cf. A001097, A001359, A006512, A014574.
%Y A138716 Cf. A138755, A139777, A139780.
%K A138716 nonn
%O A138716 1,1
%A A138716 _Vladimir Joseph Stephan Orlovsky_, May 15 2008
%E A138716 More terms from _Amiram Eldar_, Dec 22 2019