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A207330 Array of the orders Modd p, p a prime.

%I A207330 #14 Sep 17 2012 12:25:36
%S A207330 1,1,1,2,1,3,3,1,5,5,5,5,1,3,2,6,3,6,1,8,8,8,4,8,2,4,1,9,9,3,9,3,9,9,
%T A207330 9,1,11,11,11,11,11,11,11,11,11,11,1,14,7,7,7,14,7,14,2,14,14,7,7,14,
%U A207330 1,15,3,15,15,15,15,5,15,15,15,5,3,5,5,1,9,18,9
%N A207330 Array of the orders Modd p, p a prime.
%C A207330 For Modd n (not to be confused with mod n) see a comment on A203571.
%C A207330 The row lengths sequence of this array is 1 for row n=1, and (p(n)-1)/2, with p(n):=A000040(n) (the primes), for row n>1.
%C A207330 A primitive root has order delta(p) = (p-1)/2 (delta is given by A055034).
%F A207330 a(n,m) = (multiplicative) order Modd p(n) of 2*m-1, for m=1,...,(p(n)-1)/2, with p(n):= A000040(n) (the primes), n>1, and for a(1,1) = 1 for the prime 2.
%e A207330 n, p(n)/m  1  2  3  4  5  6  7  8  9 10 11 12 13 14 ...
%e A207330      2m-1: 1  3  5  7  9 11 13 15 17 19 21 23 25 27 ...
%e A207330 1,   2:    1
%e A207330 2,   3:    1
%e A207330 3,   5:    1  2
%e A207330 4,   7:    1  3  3
%e A207330 5,  11:    1  5  5  5  5
%e A207330 6,  13:    1  3  2  6  3  6
%e A207330 7,  17:    1  8  8  8  4  8  2  4
%e A207330 8,  19:    1  9  9  3  9  3  9  9  9
%e A207330 9,  23:    1 11 11 11 11 11 11 11 11 11 11
%e A207330 10, 29:    1 14  7  7  7 14  7 14  2 14 14  7  7 14
%e A207330 ...
%e A207330 a(6,4) = 6 because 7^1 = 7, 7^2 = 49, 49 (Modd 13) := -49 (mod 13) = 3, 7^3 == 7*3 = 21,
%e A207330 21 (Modd 13) := -21 (mod 13) = 5, 7^4 == 7*5 = 35, 35 (Modd 13) = 35 (mod 13) = 9,
%e A207330 7^5 == 7*9=63, 63 (Modd 13):= 63 (mod 13) = 11, 7^6 == 7*11 = 77, 77 (Modd 13) := -77 (mod 13) = 1.
%e A207330 Row n=5: all 2*m-1, m>1, are primitive roots. The smallest positive one is 3.
%e A207330 Row n=6: only 7 and 11 are primitive roots. The smallest one is 7.
%Y A207330 Cf. A086145 (mod n case).
%K A207330 nonn,easy,tabf
%O A207330 1,4
%A A207330 _Wolfdieter Lang_, Mar 27 2012