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A207330 Array of the orders Modd p, p a prime. 0
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, 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, 1, 15, 3, 15, 15, 15, 15, 5, 15, 15, 15, 5, 3, 5, 5, 1, 9, 18, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

For Modd n (not to be confused with mod n) see a comment on A203571.

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.

A primitive root has order delta(p) = (p-1)/2 (delta is given by A055034).

LINKS

Table of n, a(n) for n=1..79.

FORMULA

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.

EXAMPLE

n, p(n)/m  1  2  3  4  5  6  7  8  9 10 11 12 13 14 ...

     2m-1: 1  3  5  7  9 11 13 15 17 19 21 23 25 27 ...

1,   2:    1

2,   3:    1

3,   5:    1  2

4,   7:    1  3  3

5,  11:    1  5  5  5  5

6,  13:    1  3  2  6  3  6

7,  17:    1  8  8  8  4  8  2  4

8,  19:    1  9  9  3  9  3  9  9  9

9,  23:    1 11 11 11 11 11 11 11 11 11 11

10, 29:    1 14  7  7  7 14  7 14  2 14 14  7  7 14

...

a(6,4) = 6 because 7^1 = 7, 7^2 = 49, 49 (Modd 13) := -49 (mod 13) = 3, 7^3 == 7*3 = 21,

21 (Modd 13) := -21 (mod 13) = 5, 7^4 == 7*5 = 35, 35 (Modd 13) = 35 (mod 13) = 9,

7^5 == 7*9=63, 63 (Modd 13):= 63 (mod 13) = 11, 7^6 == 7*11 = 77, 77 (Modd 13) := -77 (mod 13) = 1.

Row n=5: all 2*m-1, m>1, are primitive roots. The smallest positive one is 3.

Row n=6: only 7 and 11 are primitive roots. The smallest one is 7.

CROSSREFS

Cf. A086145 (mod n case).

Sequence in context: A274705 A257243 A097351 * A048600 A100578 A061315

Adjacent sequences:  A207327 A207328 A207329 * A207331 A207332 A207333

KEYWORD

nonn,easy,tabf

AUTHOR

Wolfdieter Lang, Mar 27 2012

STATUS

approved

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Last modified January 29 16:58 EST 2020. Contains 331347 sequences. (Running on oeis4.)