A133518 Smallest k such that p(n)^3 + k is prime where p(n) is the n-th prime.

3, 2, 2, 4, 30, 6, 6, 4, 30, 2, 12, 18, 6, 24, 14, 14, 12, 10, 16, 2, 6, 4, 2, 14, 54, 6, 4, 18, 4, 2, 30, 26, 56, 10, 24, 12, 24, 10, 30, 2, 18, 6, 26, 24, 14, 28, 18, 10, 14, 10, 12, 24, 16, 6, 18, 2, 20, 6, 4, 12, 4, 6, 10, 2, 6, 14, 16, 4, 18, 10, 14, 14, 16, 24, 4, 12, 32, 16, 50, 12, 2

Offset: 1

Author

Carl R. White, Sep 14 2007

Keywords

• nonn
• easy

Examples

			p(1)=2, 2^3 = 8. for even k, 2^r + k is even and thus not prime, so we only need consider odd k.
for k = 1: 8 + 1 = 9, which is 3^2 and not prime.
for k = 3: 8 + 3 = 11, which is prime, so 3 is the smallest number that can be added to 8 to make a new prime.
Hence a(1) = 3.
		

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A030078, A054271, A091666, A133517, A133519, A133520, A133521, A133522, (A001223).

Programs

Magma

[NextPrime(p^3)-p^3: p in PrimesUpTo(500)]; // Bruno Berselli, Sep 03 2013

Mathematica

Table[NextPrime[Prime[n]^3] - Prime[n]^3, {n, 100}] (* Bruno Berselli, Sep 03 2013 *)

PARI

a(n) = {k = 0; p3 = prime(n)^3; while (! isprime(p3+k), k++); k;} \\ Michel Marcus, Sep 03 2013

PARI

a(n) = {p3 = prime(n)^3; nextprime(p3) - p3;} \\ Michel Marcus, Sep 03 2013