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 A281437 #25 Feb 16 2025 08:33:39 %S A281437 47,97,197,347,547,797,1097,1447,1847,2297,2797,3347,3947,4597,5297, %T A281437 6047,8597,9547,11597,12697,17597,18947,20347,23297,24847,28097,31547, %U A281437 33347,37097,39047,41047,45197,49547,51797,61297,66347,68947,71597,74297,77047,79847 %N A281437 Primes of the form 25*n^2 + 25*n + 47. %C A281437 The first 16 terms correspond to n from 0 to 15, which makes 25*n^2 + 25*n + 47 a prime-generating polynomial (see the link). %C A281437 This is a prime-generating polynomial of the form s*n^2 + s*n + p, where s=k^2 and p is prime with s and p containing at most two digits. Prime-generating polynomials of this kind arise for k=1,2,3,5,7. This is the case of k=5; it generates most primes in a row out of the prime k's listed, with 12 for k=3,7, and 14 for k=2. See also A005846 and A007635 (k=1), and A048988 (k=2). %C A281437 All terms are of the form 10m+7, with their next-to-last digits being 4 or 9. %H A281437 Robert Israel, <a href="/A281437/b281437.txt">Table of n, a(n) for n = 1..10000</a> %H A281437 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Prime-GeneratingPolynomial.html">Prime-Generating Polynomial</a> %e A281437 197 is a term as it is a prime corresponding to n=2: 25*4 + 25*2 + 47 = 197. %p A281437 select(isprime, [seq(25*n^2 + 25*n + 47, n=0..200)]); # _Robert Israel_, Dec 12 2024 %t A281437 Select[Range[0,100]//25#^2+25#+47&, PrimeQ] %o A281437 (PARI) for(n=0, 100, isprime(p=25*n^2+25*n+47)&& print1(p ", ")) %Y A281437 Cf. A000040 (primes), A005846, A007635, A048988, A292578 (similar prime-generating sequences). %K A281437 nonn %O A281437 1,1 %A A281437 _Waldemar Puszkarz_, Oct 05 2017