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

2,1

Links

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

Example

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.

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}]

Prog

(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
(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

Crossrefs

Cf. A172989

Sequence in context: A281230 A323977 A322359 * A084252 A342161 A287199

Adjacent sequences: A172987 A172988 A172989 * A172991 A172992 A172993

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 07 2010

Extensions

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

Status

approved