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.

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.

Links

Table of n, a(n) for n=1..100.

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

Adjacent sequences: A084926 A084927 A084928 * A084930 A084931 A084932

Keyword

nonn

Author

T. D. Noe, Jun 12 2003

Status

approved