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

1,1

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A345055 A247501 A192183 * A120729 A205139 A092743

Adjacent sequences: A133515 A133516 A133517 * A133519 A133520 A133521

Keyword

nonn,easy

Author

Carl R. White, Sep 14 2007

Status

approved