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 A356684 #25 Jul 30 2025 09:44:33 %S A356684 -1,-1,1,7,23,73,277,1355,8347,61573,523913,5024167,53479135, %T A356684 624890417,7946278813,109195935523,1612048228547,25439293045885, %U A356684 427278358483537,7609502950269503,143217213477235783,2840152418116022377 %N A356684 a(n) = (n-1)*a(n-1) - n*a(n-2), with a(1) = a(2) = -1. %H A356684 Mohammed Bouras, <a href="https://www.ssmrmh.ro/wp-content/uploads/2022/08/A-NEW-SEQUENCE-OF-PRIME-NUMBERS.pdf">A new sequence of prime numbers</a>, Romanian Math. Mag. (15 August 2022). See Table 1 p. 1. %H A356684 Mohammed Bouras, <a href="https://easychair.org/publications/preprint/k83H">A New Sequence of Prime Numbers</a>, EasyChair Preprint 8686, 2022. %F A356684 a(n) = A051403(n-3) + n*A051403(n-4). %F A356684 a(n)/(n^2 - n - 1) = 1/(2-3/(3-4/(4-5/(...(n-1)-n/(n-(n+1)))))), for n >= 2. %t A356684 a[1]=a[2]=-1; a[n_]:=a[n]=(n-1)a[n-1]-n a[n-2]; Array[a,22] (* _Stefano Spezia_, Aug 23 2022 *) %o A356684 (PARI) a(n) = if(n<=2, -1, 1/2*((n-1)*sum(k=0,n-3,k!) + n*(n-2)*sum(k=0,n-4,k!))) \\ _Jianing Song_, Oct 15 2022, following the formula above %Y A356684 Cf. A051403, A356247. %K A356684 sign,easy %O A356684 1,4 %A A356684 _Mohammed Bouras_, Aug 22 2022