This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A068828 #20 Jun 19 2022 18:30:27
%S A068828 2,3,7,13,19,23,31,43,47,61,73,83,89,103,109,113,131,139,151,167,181,
%T A068828 193,199,229,233,241,271,283,293,313,317,337,349,353,359,383,389,401,
%U A068828 409,421,433,443,449,463,467,491,503,509,523,547,571,577,601,619,643
%N A068828 Geometrically weak primes: primes that are smaller than the geometric mean of their neighbors (2 is included by convention).
%C A068828 Or, bad primes (version 1): primes not in A046869. - _Jonathan Vos Post_, Aug 20 2007
%C A068828 The idea can be extended by defining a geometrically weak prime of order k to be a prime which is less than the geometric mean of r neighbors on both sides for all r = 1 to k and not true for r = k+1. A similar extension could be defined for the sequence A051635.
%C A068828 It is easy to show that, except for the twin prime pair (3,5), the larger prime of every twin prime pair is in this sequence. The smaller prime of the pair is always in A046869. - _T. D. Noe_, Feb 19 2008
%H A068828 T. D. Noe, <a href="/A068828/b068828.txt">Table of n, a(n) for n=1..10000</a>
%F A068828 prime(k)^2 <= prime(k-1)*prime(k+1).
%e A068828 23 belongs to this sequence as 23^2 = 529 < 19*29 = 551.
%t A068828 Join[{2}, Prime[Select[Range[2, 120], Prime[ # ]^2 <= Prime[ # - 1]*Prime[ # + 1]&]]] (* _Stefan Steinerberger_, Aug 21 2007 *)
%t A068828 Join[{2},Transpose[Select[Partition[Prime[Range[500]],3,1],#[[2]]< GeometricMean[ {#[[1]],#[[3]]}]&]][[2]]] (* _Harvey P. Dale_, Apr 05 2014 *)
%Y A068828 Cf. A051634, A051635, A006562, A000040, A046869.
%K A068828 easy,nonn
%O A068828 1,1
%A A068828 _Amarnath Murthy_, Mar 08 2002
%E A068828 Corrected and extended by _Stefan Steinerberger_, Aug 21 2007
%E A068828 Edited by _N. J. A. Sloane_, Feb 19 2008