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A084929
If the numbers 1 to n^3 are arranged in a cubic array, a(n) is the minimum number of primes in each column of the n^2 columns in the "north-south view" that can have primes.
2
0, 1, 1, 1, 0, 2, 0, 1, 0, 2, 0, 3, 0, 2, 1, 1, 0, 3, 0, 2, 1, 2, 0, 5, 0, 3, 0, 3, 0, 7, 0, 2, 1, 2, 0, 5, 0, 3, 2, 4, 0, 8, 0, 1, 2, 4, 0, 6, 0, 4, 2, 4, 0, 6, 1, 5, 2, 3, 1, 10, 0, 4, 4, 3, 1, 9, 0, 5, 3, 9, 0, 9, 1, 4, 3, 5, 2, 8, 1, 6, 2, 4, 1, 13, 2, 6, 3, 7, 1, 14, 2, 6, 3, 5, 2, 12, 1, 9, 4, 9
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
Cf. A083382, A083414, A084927 (top view), A084928 (east-west view).
Sequence in context: A322983 A208459 A144764 * A293575 A054014 A158945
KEYWORD
nonn
AUTHOR
T. D. Noe, Jun 12 2003
STATUS
approved