OFFSET
1,6
COMMENTS
The first column is (1,4,7), the second is (2,5,8), etc. Only columns whose tops are relatively prime to n are counted. In this case, columns starting with 3, 12 and 21 cannot have primes. a(n) = 0 for n = 1, 9, 25, 27, 35, 49 and the primes from 5 to 71, except 59. It appears that a(n) > 0 for n > 109. This has been confirmed up to n = 1000.
REFERENCES
See A083382 for references and links to the two-dimensional case.
MATHEMATICA
Table[minP=n; Do[c=a+(b-1)n^2; If[GCD[c, n]==1, s=0; Do[If[PrimeQ[c+(r-1)*n], s++ ], {r, n}]; minP=Min[s, minP]], {a, n}, {b, n}]; minP, {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Jun 12 2003
STATUS
approved