The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
See A139366 for another version.
Sequence in context: A284256 A354841 A339772 * A243753 A219238 A025918
KEYWORD
nonn,easy,tabl
AUTHOR
Eric Chen, Dec 29 2014
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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