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 A050268 #36 Feb 16 2025 08:32:40
%S A050268 2753,1979,1277,647,89,359,953,1619,2357,3167,4049,5003,6029,7127,
%T A050268 8297,9539,10853,12239,13697,15227,16829,18503,20249,22067,23957,
%U A050268 25919,27953,30059,32237,34487,36809,41669,44207,46817,49499,52253
%N A050268 Primes of the form 36*k^2 - 810*k + 2753, listed in order of increasing parameter k >= 0.
%C A050268 The sequence of primes of this form, in order of increasing size, would read: 89, 359, 647, 953, 1277, 1619, 1979, 2357, 2753, ... - _M. F. Hasler_, Jan 18 2015
%C A050268 The polynomial is a transformed version of the polynomial P(x) = 36*x^2 + 18*x - 1801 whose absolute value gives 45 distinct primes for -33 <= x <= 11, found by Ruby in 1989. In the present sequence only positive values of the polynomial are taken into account. A117081 provides also the negative function values. - _Hugo Pfoertner_, Dec 13 2019
%D A050268 Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag New York, 2004.
%H A050268 Vincenzo Librandi, <a href="/A050268/b050268.txt">Table of n, a(n) for n = 1..10000</a>
%H A050268 Jitender Singh, <a href="https://arxiv.org/abs/2411.18366">Prime numbers and factorization of polynomials</a>, arXiv:2411.18366 [math.NT], 2024.
%H A050268 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>.
%p A050268 t1:=[seq(36*n^2 - 810*n + 2753,n=0..100)]; t2:=[]; for i from 1 to nops(t1) do if isprime(t1[i]) then t2:=[op(t2),t1[i]]; fi; od: t2; # _N. J. A. Sloane_
%t A050268 Select[Table[36n^2-810n+2753,{n,0,2000}],PrimeQ] (* _Vincenzo Librandi_, Dec 08 2011 *)
%o A050268 (PARI) select(isprime, vector(1000, n, 36*n^2-810*n+2753)) \\ _Charles R Greathouse IV_, Feb 14 2011
%o A050268 (Magma) [a: n in [0..100] | IsPrime(a) where a is 36*n^2 - 810*n + 2753]; // _Vincenzo Librandi_, Dec 08 2011
%Y A050268 Cf. A022464, A117081.
%K A050268 nonn,easy,less
%O A050268 1,1
%A A050268 _Eric W. Weisstein_
%E A050268 Definition corrected by _M. F. Hasler_, Jan 18 2015