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A084928 If the numbers 1 to n^3 are arranged in a cubic array, a(n) is the minimum number of primes in each row of the n^2 rows in the "east-west view" that can have primes.

%I A084928 #8 Jan 02 2019 11:54:19
%S A084928 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,
%T A084928 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,
%U A084928 1,1,1,0,0,0,0,0,0,0,0,1,0,1,0,0,0,1,0,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1,1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,2
%N A084928 If the numbers 1 to n^3 are arranged in a cubic array, a(n) is the minimum number of primes in each row of the n^2 rows in the "east-west view" that can have primes.
%C A084928 This is a three-dimensional generalization of A083382.
%D A084928 See A083382 for references and links to the two-dimensional case.
%H A084928 Antti Karttunen, <a href="/A084928/b084928.txt">Table of n, a(n) for n = 1..900</a>
%e A084928 For the case n=3, the numbers are arranged in a cubic array as follows:
%e A084928 1..2..3........10.11.12........19.20.21
%e A084928 4..5..6........13.14.15........22.23.24
%e A084928 7..8..9........16.17.18........25.26.27
%e A084928 The first row is (1,2,3), the second is (4,5,6), etc. Surprisingly, a(n) = 0 for all n from 3 to 66. It appears that a(n) > 0 for n > 128. This has been confirmed up to n = 1000.
%t A084928 Table[minP=n; Do[s=0; Do[If[PrimeQ[n*(c-1)+r], s++ ], {r, n}]; minP=Min[s, minP], {c, n^2}]; minP, {n, 100}]
%o A084928 (PARI) A084928(n) = { my(m=-1); for(i=0,(n^2)-1,my(s=sum(j=(i*n),((i+1)*n)-1,isprime(1+j))); if((m<0) || (s < m), m = s)); (m); }; \\ _Antti Karttunen_, Jan 01 2019
%Y A084928 Cf. A083382, A083414, A084927 (top view), A084929 (north-south view).
%K A084928 nonn
%O A084928 1,121
%A A084928 _T. D. Noe_, Jun 12 2003
%E A084928 More terms from _Antti Karttunen_, Jan 01 2019