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

1,1

Comments

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

Links

Table of n, a(n) for n=1..56.

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 *)

Crossrefs

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

Sequence in context: A059788 A077171 A171602 * A065384 A354217 A338567

Adjacent sequences: A155186 A155187 A155188 * A155190 A155191 A155192

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 21 2009

Status

approved