OFFSET
1,4
COMMENTS
Conjectured to be always positive for n>1.
Note that a(n) is large when phi(n), the number of integers relatively prime to n, is small and vice versa. - T. D. Noe, Jun 10 2003
The conjecture is true for all n <= 40000.
REFERENCES
See A083382 for references and links.
LINKS
T. D. Noe, Table of n, a(n) for n=1..2000
EXAMPLE
For n = 4 the array is
. 1 2 3 4
. 5 6 7 8
. 9 10 11 12
. 13 14 15 16
in which columns 1 and 3 contain 2 and 3 primes; therefore a(4) = 2.
MATHEMATICA
Table[minP=n; Do[If[GCD[c, n]==1, s=0; Do[If[PrimeQ[c+(r-1)*n], s++ ], {r, n}]; minP=Min[s, minP]], {c, n}]; minP, {n, 100}]
PROG
(Haskell)
a083414 n = minimum $ map c $ filter ((== 1) . (gcd n)) [1..n] where
c k = sum $ map a010051 $ enumFromThenTo k (k + n) (n ^ 2)
-- Reinhard Zumkeller, Jun 10 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 10 2003
EXTENSIONS
More terms from Vladeta Jovovic and T. D. Noe, Jun 10 2003
STATUS
approved