%I #9 May 13 2022 19:47:48
%S 23,103,1471,1609,2389,2861,4409,5011,5507,5569,6263,7793,8443,9623,
%T 11483,11971,12007,17137,17569,18457,19949,21701,23017,23279,23743,
%U 24907,26321,27943,29017,29191,29641,30881,32059,32713,34213,34583,35153,36523,36887
%N Primes p1 such that p1^2+p2^3=pp are average of twin primes. p1 and p2 consecutive primes, p1 < p2.
%t a={};Do[p1=Prime[n];p2=Prime[n+1];pp=p1^2+p2^3;If[PrimeQ[pp-1]&&PrimeQ[pp+1],AppendTo[a,p1]],{n,16^3}];Print[a];
%t atpQ[n_]:=Module[{c=First[n]^2+Last[n]^3},And@@PrimeQ[{c-1,c+1}]]; Transpose[Select[Partition[Prime[Range[5000]],2,1],atpQ]][[1]] (* _Harvey P. Dale_, Sep 11 2011 *)
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, May 15 2008
%E More terms from _Harvey P. Dale_, Sep 11 2011
%E Typo in a(39) corrected by _Seth A. Troisi_, May 13 2022