cp's OEIS Frontend

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.

A356727 Primes of the form 4*k^2 + 84*k + 43.

This page as a plain text file.
%I A356727 #22 May 07 2023 18:52:58
%S A356727 43,131,227,331,443,563,691,827,971,1123,1283,1451,1627,1811,2003,
%T A356727 2203,2411,2851,3083,3323,3571,4091,4363,4643,4931,5227,5531,5843,
%U A356727 6163,6491,6827,7523,7883,8627,9011,9403,9803,10211,10627,11483,11923,13291,13763,14243,14731,15227,15731
%N A356727 Primes of the form 4*k^2 + 84*k + 43.
%C A356727 The polynomial 4*k^2 + 84*k + 43 has prime values for k from 0 to 16. The proportion of prime numbers (23.28%) obtained among the first ten million values is slightly higher than that (22.08%) obtained with Euler's polynomial k^2 - k + 41.
%C A356727 The polynomial 4*k^2 + 84*k + 43 produces a Hardy-Littlewood constant of 7.3291180993696....
%H A356727 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime generating polynomial</a>
%t A356727 Select[Table[4k^2+84k+43,{k,0,60}],PrimeQ] (* _Harvey P. Dale_, May 07 2023 *)
%Y A356727 Cf. A005846, A221712, A331940.
%K A356727 nonn,less
%O A356727 1,1
%A A356727 _Charles Delaporte_, Aug 24 2022