OFFSET
1,6
COMMENTS
This is a three-dimensional generalization of A083414.
REFERENCES
See A083382 for references and links to the two-dimensional case.
EXAMPLE
For the case n=3, the numbers are arranged in a cubic array as follows:
1..2..3........10.11.12........19.20.21
4..5..6........13.14.15........22.23.24
7..8..9........16.17.18........25.26.27
The first column is (1,10,19), the second is (2,11,20), etc. Only columns whose tops are relatively prime to n are counted. In this case, columns starting with 3, 6 and 9 cannot have primes. a(n) = 0 for n = 1, 25, 55 and the primes from 5 to 83, except 67 and 79. It appears that a(n) > 0 for n > 83. This has been confirmed up to n = 1000.
MATHEMATICA
Table[minP=n; Do[If[GCD[c, n]==1, s=0; Do[If[PrimeQ[c+(r-1)*n^2], s++ ], {r, n}]; minP=Min[s, minP]], {c, n^2}]; minP, {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Jun 12 2003
STATUS
approved