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 A250211 Square array read by antidiagonals: A(m,n) = multiplicative order of m mod n, or 0 if m and n are not coprime. 3
 1, 1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 2, 4, 1, 1, 0, 2, 0, 4, 0, 1, 1, 1, 0, 1, 2, 0, 3, 1, 1, 0, 1, 0, 0, 0, 6, 0, 1, 1, 1, 2, 2, 1, 2, 3, 2, 6, 1, 1, 0, 0, 0, 4, 0, 6, 0, 0, 0, 1, 1, 1, 1, 1, 4, 1, 2, 2, 3, 4, 10, 1, 1, 0, 2, 0, 2, 0, 0, 0, 6, 0, 5, 0, 1, 1, 1, 0, 2, 0, 0, 1, 2, 0, 0, 5, 0, 12, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 COMMENTS Read by antidiagonals: m\n 1 2 3 4 5 6 7 8 9 10 11 12 13 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 0 2 0 4 0 3 0 6 0 10 0 12 3 1 1 0 2 4 0 6 2 0 4 5 0 3 4 1 0 1 0 2 0 3 0 3 0 5 0 6 5 1 1 2 1 0 2 6 2 6 0 5 2 4 6 1 0 0 0 1 0 2 0 0 0 10 0 12 7 1 1 1 2 4 1 0 2 3 4 10 2 12 8 1 0 2 0 4 0 1 0 2 0 10 0 4 9 1 1 0 1 2 0 3 1 0 2 5 0 3 10 1 0 1 0 0 0 6 0 1 0 2 0 6 11 1 1 2 2 1 2 3 2 6 1 0 2 12 12 1 0 0 0 4 0 6 0 0 0 1 0 2 13 1 1 1 1 4 1 2 2 3 4 10 1 0 etc. A(m,n) = Least k>0 such that m^k=1 (mod n), or 0 if no such k exists. It is easy to prove that column n has period n. A(1,n) = 1, A(m,1) =1. If A(m,n) differs from 0, it is period length of 1/n in base m. The maximum number in column n is psi(n) (A002322(n)), and all numbers in column n (except 0) divide psi(n), and all factors of psi(n) are in column n. Except the first row, every row contains all natural numbers. LINKS Table of n, a(n) for n=1..105. EXAMPLE A(3,7) = 6 because: 3^0 = 1 (mod 7) 3^1 = 3 (mod 7) 3^2 = 2 (mod 7) 3^3 = 6 (mod 7) 3^4 = 4 (mod 7) 3^5 = 5 (mod 7) 3^6 = 1 (mod 7) ... And the period is 6, so A(3,7) = 6. MAPLE f:= proc(m, n) if igcd(m, n) <> 1 then 0 elif n=1 then 1 else numtheory:-order(m, n) fi end proc: seq(seq(f(t-j, j), j=1..t-1), t=2..65); # Robert Israel, Dec 30 2014 MATHEMATICA a250211[m_, n_] = If[GCD[m, n] == 1, MultiplicativeOrder[m, n], 0] Table[a250211[t-j, j], {t, 2, 65}, {j, 1, t-1}] CROSSREFS Cf. A002322, A111076, A111725, A001918, A008330, A007733, A002326, A007732, A051626, A066799. See A139366 for another version. Sequence in context: A284256 A354841 A339772 * A243753 A219238 A025918 Adjacent sequences: A250208 A250209 A250210 * A250212 A250213 A250214 KEYWORD nonn,easy,tabl AUTHOR Eric Chen, Dec 29 2014 STATUS approved

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Last modified May 21 22:16 EDT 2024. Contains 372741 sequences. (Running on oeis4.)