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 A033235 #33 Jul 08 2025 19:46:55 %S A033235 59,71,199,229,251,269,311,379,389,499,509,631,661,691,751,839,881, %T A033235 929,1049,1061,1171,1181,1279,1321,1409,1439,1499,1571,1609,1699,1721, %U A033235 1741,1901,1951,2029,2069,2269 %N A033235 Primes of the form x^2 + 55*y^2. %C A033235 Also primes of the form x^2 - xy + 14y^2 with x and y nonnegative. - _T. D. Noe_, May 08 2005 %C A033235 From _Lechoslaw Ratajczak_, Apr 09 2017: (Start) %C A033235 Conjecture: consecutive elements of this sequence are consecutive primes satisfying the congruence b(k) == 1 (mod k) for k>0, where b(k) is recursive sequence defined as follows: b(k) = -b(k-1) - b(k-2) + b(k-3) - b(k-4) with b(0)=2, b(1)=1, b(2)=0, b(3)=-1. %C A033235 (b(59) - 1) mod 59 = (-496870918 - 1) mod 59 = 0, 59 = a(1). %C A033235 (b(71) - 1) mod 71 = (88081764473 - 1) mod 71 = 0, 71 = a(2). %C A033235 For 10^6 consecutive positive integers there are 9748 prime solutions and 5 nonprime (1, 586, 2935, 17161, 429737) solutions of the congruence. (End) %D A033235 David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989. %H A033235 Vincenzo Librandi and Ray Chandler, <a href="/A033235/b033235.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi] %H A033235 N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references) %t A033235 QuadPrimes2[1, 0, 55, 10000] (* see A106856 *) %K A033235 nonn,easy %O A033235 1,1 %A A033235 _N. J. A. Sloane_