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.
0, 99, 14, 1, 2, 73, 33, 10, 137, 277856, 1
Offset: 1
Examples
a(1) = 0 as prime(1) + 1 = 2 + 1 = 3, which is divisible by prime(2) = 3. a(3) = 14 as prime(3) * ... * prime(17) + 1 = 320460058359035439846, which is divisible by prime(18) = 61. a(10) = 277856 as prime(10) * ... * prime(277866) + 1 = 645399...451368 (a number with 1701172 digits), which is divisible by prime(277867) = 3919259. a(11) = 1 as prime(11) * prime(12) + 1 = 31 * 37 + 1 = 1148, which is divisible by prime(13) = 41.
Programs
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Python
from sympy import prime, nextprime def A360376(n): p = prime(n) s, k = p, 0 while (s+1)%(p:=nextprime(p)): k += 1 s *= p return k # Chai Wah Wu, Feb 07 2023
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