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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. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,121

COMMENTS

This is a three-dimensional generalization of A083382.

REFERENCES

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

LINKS

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

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 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.

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}]

PROG

(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

CROSSREFS

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

Sequence in context: A005088 A076142 A084904 * A112316 A112802 A137979

Adjacent sequences:  A084925 A084926 A084927 * A084929 A084930 A084931

KEYWORD

nonn

AUTHOR

T. D. Noe, Jun 12 2003

EXTENSIONS

More terms from Antti Karttunen, Jan 01 2019

STATUS

approved

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Last modified July 9 11:58 EDT 2020. Contains 335543 sequences. (Running on oeis4.)