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 A145202 #17 Feb 16 2025 08:33:09
%S A145202 653,661,677,701,733,773,821,877,941,1013,1093,1181,1277,1381,1493,
%T A145202 1613,1741,1877,2333,2677,2861,3253,3461,3677,4133,4373,4621,4877,
%U A145202 5413,5693,5981,6277,6581,7213,7541,7877,8221,8573,8933,9677,10061,10453,10853
%N A145202 Primes of form 4*n^2 + 4*n + 653.
%C A145202 First 18 terms are for n from 0 through 17, next terms are for n = 20, 22, 23, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 38, 40, ...
%C A145202 The sequence of n such that 4*n^2 + 4*n + 653 is composite starts 18, 19, 21, 24, 28, 33, 39, 46, 54, 60, 61, 62, 63, 65, 67, 72, 73, 75, 81, 82, 84, 85, 86, 93, 95, 96, 100, ...
%C A145202 These primes are in A000414. [_Bruno Berselli_, Apr 20 2014]
%H A145202 Vincenzo Librandi, <a href="/A145202/b145202.txt">Table of n, a(n) for n = 1..1000</a>
%H A145202 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a>
%e A145202 a(18) = 4*17^2 + 4*17 + 653 = 1877.
%t A145202 Select[Table[4 n^2 + 4 n + 653, {n, 0, 100}], PrimeQ] (* _Vincenzo Librandi_, Apr 21 2014 *)
%o A145202 (PARI) {for(n=0, 50, if(isprime(p=4*n^2+4*n+653), print1(p, ",")))}
%o A145202 (Magma) [a: n in [0..100] | IsPrime(a) where a is 4*n^2 + 4*n + 653]; // _Vincenzo Librandi_, Apr 21 2014
%Y A145202 A145125 is essentially the same sequence.
%Y A145202 Cf. A005846 (primes of form n^2 + n + 41).
%K A145202 nonn
%O A145202 1,1
%A A145202 _Klaus Brockhaus_, Oct 04 2008