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%I #4 May 01 2021 11:42:22
%S 3,5,7,13,19,23,31,43,47,53,61,73,83,89,103,109,113,131,139,151,157,
%T 167,173,181,193,199,211,229,233,241,257,263,271,283,293,313,317,337,
%U 349,353,359,373,383,389,401,409,421,433,443,449,463,467,491,503,509,523
%N Square-weak primes.
%C 5^2 = 25 < 29 = (3^2+7^2)/2, ...
%t lst={};Do[p0=Prime[n];p1=Prime[n+1];p2=Prime[n+2];If[p1^2<(p0^2+p2^2)/2,AppendTo[lst,p1]],{n,5!}];lst
%t Select[Partition[Prime[Range[100]],3,1],#[[2]]^2<(#[[1]]^2+#[[3]]^2)/2&][[All,2]] (* _Harvey P. Dale_, May 01 2021 *)
%Y Cf. A045536, A005384, A051634, A006562, A051635, A155188
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Jan 21 2009
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