A155189 Square-weak primes.

3, 5, 7, 13, 19, 23, 31, 43, 47, 53, 61, 73, 83, 89, 103, 109, 113, 131, 139, 151, 157, 167, 173, 181, 193, 199, 211, 229, 233, 241, 257, 263, 271, 283, 293, 313, 317, 337, 349, 353, 359, 373, 383, 389, 401, 409, 421, 433, 443, 449, 463, 467, 491, 503, 509, 523

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Keywords

• nonn

Comments

5^2 = 25 < 29 = (3^2+7^2)/2, ...

Crossrefs

Cf. A045536, A005384, A051634, A006562, A051635, A155188

Programs

Mathematica

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
Select[Partition[Prime[Range[100]],3,1],#[[2]]^2<(#[[1]]^2+#[[3]]^2)/2&][[All,2]] (* Harvey P. Dale, May 01 2021 *)