A133520 Smallest k such that p(n)^4 + k is prime where p(n) is the n-th prime.

1, 2, 6, 10, 12, 10, 16, 16, 6, 12, 18, 16, 12, 28, 6, 22, 6, 16, 6, 16, 6, 16, 30, 6, 16, 42, 22, 42, 28, 52, 22, 16, 28, 10, 28, 70, 30, 42, 78, 36, 12, 42, 6, 12, 40, 12, 12, 16, 16, 16, 18, 10, 6, 22, 60, 46, 76, 46, 18, 126, 12, 22, 22, 6, 16, 16, 22, 18, 120, 22, 12, 6, 6, 36

Offset: 1

Author

Carl R. White, Sep 14 2007

Keywords

• easy
• nonn

Examples

			p(2)=3, 3^4 = 81; 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: 81 + 2 = 83, which is prime, so 2 is the smallest number that can be added to 81 to make a new prime.
Hence a(2) = 2.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A030814, A054271, A091666, A133517, A133518, A133519, A133521, A133522, (A001223).

Programs

Mathematica

NextPrime[#]-#&/@(Prime[Range[80]]^4) (* Harvey P. Dale, May 17 2015 *)