A133522 - OEIS

A133522

Smallest k such that p(n)^5 + k is prime where p(n) is the n-th prime.

5, 8, 12, 4, 2, 6, 20, 22, 8, 8, 12, 22, 26, 30, 20, 20, 74, 52, 22, 26, 4, 22, 6, 42, 40, 8, 58, 44, 42, 8, 40, 6, 36, 28, 2, 28, 6, 4, 20, 14, 2, 12, 8, 46, 2, 40, 10, 4, 110, 12, 18, 44, 42, 6, 24, 20, 8, 28, 46, 2, 18, 6, 60, 36, 24, 2, 18, 4, 24, 48, 6, 30, 6, 6, 22, 6, 2, 6, 2, 40, 2

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..81.

EXAMPLE

p(2)=3, 3^5 = 243; for odd k and n > 1, p(n)^r - k is even and thus not prime, so we only need consider even k.

for k = 2: 243 + 2 = 245, which is 5 * 7^2 and not prime.

for k = 4: 243 + 4 = 247, which is 13 * 19, also not prime.

for k = 6: 243 + 6 = 249, which is 3 * 83, also not prime.

for k = 8: 243 + 8 = 251, which is prime, so 8 is the smallest number that can be added to 243 to make another prime.

Hence a(2) = 8.