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 A083522 #7 Oct 19 2017 03:14:16 %S A083522 1,1,1,0,3,3,4,4,6,2,1,10,5,3,9,6,6,4,5,8,6,7,19,25,11,2,1,3,9,23,7,7, %T A083522 39,5,7,2,1,5,78,2,1,15,19,12,17,6,3,14,8,21,23,17,14,40,16,6,8,13,15, %U A083522 5,15,82,46,51,39,43,6,11,61,57,16,2,1,26,54,2,1,13,4,62,31,69,27,155,21 %N A083522 Smallest k such that k*(k+1)*(k+2)*...*(k+n-1) + 1 is prime, or 0 if no such number exists. %C A083522 The product of four consecutive integers + 1 is always composite (a square), so a(4) = 0. Are there any more zeros in the sequence? %C A083522 Since rather large numbers (up to 193 digits) are encountered in the computation, the Pocklington-Lehmer "P-1" primality test is used, as implemented in PARI 2.1.3. %e A083522 1*2*3*4*5 + 1 = 121 = 11*11 and 2*3*4*5*6 + 1 = 721 = 7*103 are composite, but 3*4*5*6*7 + 1 = 2521 is prime, so a(5) = 3. %o A083522 (PARI) m=1000; for(n=1,85,b=0; k=1; while(b<1&&k<m,if(!isprime(prod(j=k,k+n-1,j)+1,1),k++,b=1)); print1(if(k<m,k,0),",")) %Y A083522 Cf. A083520, A083521. %K A083522 nonn %O A083522 1,5 %A A083522 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 05 2003 %E A083522 Edited and extended by _Klaus Brockhaus_ and _Don Reble_, May 06 2003