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 A360376 #17 Feb 07 2023 14:14:01 %S A360376 0,99,14,1,2,73,33,10,137,277856,1 %N A360376 a(n) = minimal nonnegative k such that prime(n) * prime(n+1) * ... * prime(n+k) + 1 is divisible by prime(n+k+1), or -1 if no such k exists. %C A360376 Assuming a(12) exists it is greater than 2.25 million. %e A360376 a(1) = 0 as prime(1) + 1 = 2 + 1 = 3, which is divisible by prime(2) = 3. %e A360376 a(3) = 14 as prime(3) * ... * prime(17) + 1 = 320460058359035439846, which is divisible by prime(18) = 61. %e A360376 a(10) = 277856 as prime(10) * ... * prime(277866) + 1 = 645399...451368 (a number with 1701172 digits), which is divisible by prime(277867) = 3919259. %e A360376 a(11) = 1 as prime(11) * prime(12) + 1 = 31 * 37 + 1 = 1148, which is divisible by prime(13) = 41. %o A360376 (Python) %o A360376 from sympy import prime, nextprime %o A360376 def A360376(n): %o A360376 p = prime(n) %o A360376 s, k = p, 0 %o A360376 while (s+1)%(p:=nextprime(p)): %o A360376 k += 1 %o A360376 s *= p %o A360376 return k # _Chai Wah Wu_, Feb 07 2023 %Y A360376 Cf. A360406, A360297, A000040, A007504, A332542, A332580. %K A360376 nonn,more %O A360376 1,2 %A A360376 _Scott R. Shannon_, Feb 04 2023