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 A309027 #22 Aug 15 2021 17:11:19 %S A309027 3,11,19,43,59,179,211,283,563,619,739,1163,1499,1979,2083,2411,3011, %T A309027 3539,4259,4723,7603,8011,8219,10211,11411,12163,14011,14563,14843, %U A309027 17483,20011,23059,25579,26699,28619,29803,30203,33923,36083,36523,41539,49411,54139,55219,55763,59083 %N A309027 Prime powers of the form 12*c^2 + 4*c + 3, where c is an arbitrary integer. %C A309027 It is conjectured that all terms are prime. See Leung et al. p. 12. %C A309027 All terms up to 10^9 are prime. %C A309027 Since the Diophantine equation 12*c^2 + 4*c + 3 = x^2 has no solution, all terms p^e have either e=1 or e>=3 and odd. Up to 10^24, all terms are prime. - _Giovanni Resta_, Jul 08 2019 %C A309027 It appears that these are the primes of A271723. - _Bill McEachen_, Aug 14 2021 %H A309027 Ka Hin Leung, Koji Momihara and Qing Xiang, <a href="https://arxiv.org/abs/1907.02623">A new family of Hadamard matrices of order 4(2q^2+1)</a>, arXiv:1907.02623 [math.CO], 2019. See p. 3. %o A309027 (PARI) isok(n) = isprimepower(n) && issquare(3*n-8) && (d=sqrtint(3*n-8)) && ((frac((d-1)/6) == 0) || (frac((d+1)/6) == 0)); %Y A309027 Cf. A271723. %K A309027 nonn %O A309027 1,1 %A A309027 _Michel Marcus_, Jul 08 2019