A083382 -id:A083382 - cp's OEIS frontend

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

T. D. Noe, Jun 12 2003

nonn

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.

See A083382 for references and links to the two-dimensional case.

Cf. A083382, A083414, A084927 (top view), A084928 (east-west view).

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}]

cp's OEIS Frontend

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.

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