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 A274675 #49 May 23 2025 03:54:53
%S A274675 23,71,79,113,127,137,151,191,193,233,239,263,281,337,359,401,431,449,
%T A274675 457,463,487,569,599,617,631,641,673,743,751,809,823,863,911,919,953,
%U A274675 967,977,991,1009,1031,1033,1087,1103,1129,1201,1289,1297,1303,1327
%N A274675 Primes p such that p = x^2 + 14*y^2 or p = 2*x^2 + 7*y^2, where p != 2, 7 and x, y are integers.
%C A274675 Also primes congruent to {1, 9, 15, 23, 25, 39} mod 56.
%C A274675 From _Wolfdieter Lang_, Jun 04 2021: (Start)
%C A274675 Discriminant -8*7. The product of two entries is congruent to {1, 7} (mod 8). (Buell, p. 51, 3).
%C A274675 The given two reduced positive definite binary quadratic forms represent the odd primes, not 7, with the generic characters Legendre(p|7) = +1 and Legendre(2|p) = +1. The other two reduced forms are [3, 2, 5] and [3,-2, 5] with values -1 and -1 for these two generic characters, and give the odd primes, not 7, listed in A106915. This is related to the two genera of discriminant -56 with class number h(-56) = 4. See Buell, p. 52, 2), and Cox, p. 30.
%C A274675 There is a misprint 29 (instead of 39) in Cox (1989, ISBN 0-471-50654-0), p. 33, in eqs. (2.21) and (2.23). (End)
%C A274675 In the first US edition, there just one error, in Eq. (2.21), and it is on page 33. In the second edition this error has been corrected. - _N. J. A. Sloane_, Jun 04 2021
%D A274675 D. A. Buell, Binary Quadratic Forms. Springer-Verlag, NY, 1989, pp. 51-53.
%D A274675 David A. Cox, Primes of the Form x^2 + n y^2, John Wiley & Sons, 1st edition, 1989; 2nd edition, 2003.
%H A274675 Vincenzo Librandi, <a href="/A274675/b274675.txt">Table of n, a(n) for n = 1..1000</a>
%H A274675 Thomas R. Hagedorn, <a href="https://citeseerx.ist.psu.edu/pdf/c07a566df2876b5040dc35f1526833f6a8734166">Primes of the form x^2+ny^2 and the geometry of (convenient) numbers</a> (page 3).
%t A274675 Select[Prime@Range[300], MemberQ[{1, 9, 15, 23, 25, 39}, Mod[#, 56]] &]
%o A274675 (Magma) [p: p in PrimesUpTo(3000) | p mod 56 in {1, 9, 15, 23, 25, 39} ];
%o A274675 (PARI) is(n) = ispseudoprime(n) && #setintersect([n % 56], [1, 9, 15, 23, 25, 39])==1 \\ _Felix Fröhlich_, Jul 02 2016
%Y A274675 Cf. A033202, A106915.
%K A274675 nonn,easy
%O A274675 1,1
%A A274675 _Vincenzo Librandi_, Jul 02 2016