A172990 a(n) is the smallest k such that the two numbers n^3 +- k are primes.

3, 4, 3, 12, 17, 6, 9, 10, 9, 30, 5, 54, 33, 14, 3, 24, 11, 168, 81, 20, 9, 60, 17, 18, 3, 80, 9, 18, 73, 192, 75, 14, 63, 54, 7, 54, 255, 38, 303, 42, 11, 114, 63, 4, 33, 180, 5, 30, 93, 28, 21, 84, 115, 18, 15, 40, 9, 228, 61, 318, 171, 4, 93, 42, 5, 24, 9, 70, 51, 72, 49, 444, 3

Offset: 2

Author

Vladimir Joseph Stephan Orlovsky, Feb 07 2010

Keywords

• nonn

Examples

			Both 2^3 - 3 = 5 and 2^3 + 3 = 11 are prime, and there is no positive number k < 3 for which this is the case, so a(2) = 3; similarly,
both 3^3 -  4 =  23 and 3^3 +  4 =  31 are prime;
both 4^3 -  3 =  61 and 4^3 +  3 =  67 are prime;
both 5^3 - 12 = 113 and 5^3 + 12 = 137 are prime.
		

Links

• Marius A. Burtea, Table of n, a(n) for n = 2..5001

Crossrefs

Cf. A172989

Programs

MATLAB

m=1; for n=2:80 for k=1:1000 if and(isprime(n^3-k)==1, isprime(n^3+k)==1) sol(m)=k; m=m+1; break; end; end; end; sol % Marius A. Burtea, Jul 31 2019

Magma

sol:=[]; for m in [2..80] do k:=1; while k le 1000 and not(IsPrime(m^3-k) and IsPrime(m^3+k)) do k:=k+1; end while; sol[m-1]:=k; end for; sol; // Marius A. Burtea, Jul 31 2019

Mathematica

f[n_]:=Block[{k},If[OddQ[n],k=2,k=1];While[ !PrimeQ[n-k]||!PrimeQ[n+k],k+=2];k];Table[f[n^3],{n,2,40}]

Extensions

Name and Example section edited by Jon E. Schoenfield, Jul 31 2019