

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 "northsouth view" that can have primes.


2



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
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OFFSET

1,6


COMMENTS

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.


REFERENCES

See A083382 for references and links to the twodimensional case.


LINKS

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


MATHEMATICA

Table[minP=n; Do[c=a+(b1)n^2; If[GCD[c, n]==1, s=0; Do[If[PrimeQ[c+(r1)*n], s++ ], {r, n}]; minP=Min[s, minP]], {a, n}, {b, n}]; minP, {n, 100}]


CROSSREFS

Cf. A083382, A083414, A084927 (top view), A084928 (eastwest view).
Sequence in context: A322983 A208459 A144764 * A293575 A054014 A158945
Adjacent sequences: A084926 A084927 A084928 * A084930 A084931 A084932


KEYWORD

nonn


AUTHOR

T. D. Noe, Jun 12 2003


STATUS

approved



