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A084927 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 "top view" that can have primes. 4
0, 1, 1, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 0, 3, 0, 3, 1, 1, 0, 4, 0, 3, 1, 3, 0, 8, 0, 2, 2, 3, 1, 5, 0, 2, 1, 4, 0, 9, 0, 3, 2, 4, 0, 6, 1, 6, 2, 4, 0, 5, 0, 5, 2, 3, 0, 11, 0, 4, 3, 3, 1, 10, 1, 5, 3, 7, 0, 10, 0, 2, 4, 6, 2, 11, 1, 7, 3, 5, 0, 13, 2, 6, 4, 7, 1, 17, 2, 6, 2, 6, 2, 12, 1, 8, 4, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

This is a three-dimensional generalization of A083414.

REFERENCES

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

LINKS

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

EXAMPLE

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 column is (1,10,19), the second is (2,11,20), etc. Only columns whose tops are relatively prime to n are counted. In this case, columns starting with 3, 6 and 9 cannot have primes. a(n) = 0 for n = 1, 25, 55 and the primes from 5 to 83, except 67 and 79. It appears that a(n) > 0 for n > 83. This has been confirmed up to n = 1000.

MATHEMATICA

Table[minP=n; Do[If[GCD[c, n]==1, s=0; Do[If[PrimeQ[c+(r-1)*n^2], s++ ], {r, n}]; minP=Min[s, minP]], {c, n^2}]; minP, {n, 100}]

CROSSREFS

Cf. A083382, A083414, A084928 (east-west view), A084929 (north-south view).

Sequence in context: A178146 A305435 A114708 * A333750 A072670 A087624

Adjacent sequences:  A084924 A084925 A084926 * A084928 A084929 A084930

KEYWORD

nonn

AUTHOR

T. D. Noe, Jun 12 2003

STATUS

approved

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Last modified July 13 12:30 EDT 2020. Contains 335687 sequences. (Running on oeis4.)