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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

%I

%S 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,

%T 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,

%U 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

%N 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.

%C 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.

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

%t 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}]

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

%K nonn

%O 1,6

%A _T. D. Noe_, Jun 12 2003

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Last modified August 9 22:52 EDT 2020. Contains 336335 sequences. (Running on oeis4.)