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 A083414 Write the numbers from 1 to n^2 consecutively in n rows of length n; let c(k) = number of primes in k-th column; a(n) = minimal c(k) for gcd(k,n) = 1. 6
 0, 1, 1, 2, 1, 4, 1, 2, 3, 5, 2, 6, 1, 5, 5, 5, 2, 10, 2, 6, 5, 8, 3, 9, 5, 8, 5, 9, 4, 17, 3, 9, 7, 9, 6, 15, 4, 9, 8, 13, 4, 21, 3, 11, 10, 11, 4, 17, 5, 15, 9, 14, 5, 20, 8, 14, 9, 14, 6, 27, 6, 15, 12, 14, 9, 26, 6, 15, 12, 23, 5, 25, 3, 15, 13, 17, 8, 29, 7, 20, 12, 17, 7, 32 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A083415 and A083382 for primes in rows. A084927 generalizes this to three dimensions. Cf. A010051. Sequence in context: A072064 A105498 A179289 * A171174 A171173 A268671 Adjacent sequences:  A083411 A083412 A083413 * A083415 A083416 A083417 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

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Last modified April 8 21:31 EDT 2020. Contains 333329 sequences. (Running on oeis4.)