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

1,2

Comments

Assuming a(12) exists it is greater than 2.25 million.

Links

Table of n, a(n) for n=1..11.

Example

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.

Prog

(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

Crossrefs

Cf. A360406, A360297, A000040, A007504, A332542, A332580.

Sequence in context: A097846 A246222 A309232 * A304140 A305046 A316732

Adjacent sequences: A360373 A360374 A360375 * A360377 A360378 A360379

Keyword

nonn,more

Author

Scott R. Shannon, Feb 04 2023

Status

approved