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.

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, 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, 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

Offset: 1

Author

T. D. Noe, Jun 12 2003

Keywords

• nonn

Comments

This is a three-dimensional generalization of A083382.

Examples

			For the case n=3, the numbers are arranged in a cubic array as follows:
1..2..3........10.11.12........19.20.21
4..5..6........13.14.15........22.23.24
7..8..9........16.17.18........25.26.27
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.
		

References

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..900

Crossrefs

Cf. A083382, A083414, A084927 (top view), A084929 (north-south view).

Programs

Mathematica

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}]

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

Extensions

More terms from Antti Karttunen, Jan 01 2019