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A008830 Discrete logarithm of n to the base 2 modulo 11.

%I A008830 #15 Sep 08 2022 08:44:36
%S A008830 0,1,8,2,4,9,7,3,6,5
%N A008830 Discrete logarithm of n to the base 2 modulo 11.
%C A008830 Equivalently, a(n) is the multiplicative order of n with respect to base 2 (modulo 11), i.e., a(n) is the base-2 logarithm of the smallest k such that 2^k mod 11 = n. - _Jon E. Schoenfield_, Aug 21 2021
%D A008830 I. M. Vinogradov, Elements of Number Theory, p. 220.
%H A008830 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DiscreteLogarithm.html">Discrete Logarithm</a>.
%F A008830 2^a(n) == n (mod 11). - _Michael S. Branicky_, Aug 13 2021
%e A008830 From _Jon E. Schoenfield_, Aug 21 2021: (Start)
%e A008830 Sequence is a permutation of the 10 integers 0..9:
%e A008830    k     2^k  2^k mod 11
%e A008830   --  ------  ----------
%e A008830    0       1           1  so a(1)  =  0
%e A008830    1       2           2  so a(2)  =  1
%e A008830    2       4           4  so a(4)  =  2
%e A008830    3       8           8  so a(8)  =  3
%e A008830    4      16           5  so a(5)  =  4
%e A008830    5      32          10  so a(10) =  5
%e A008830    6      64           9  so a(9)  =  6
%e A008830    7     128           7  so a(7)  =  7
%e A008830    8     256           3  so a(3)  =  8
%e A008830    9     512           6  so a(6)  =  9
%e A008830   10    1024           1
%e A008830 but a(1) = 0, so the sequence is finite with 10 terms.
%e A008830 (End)
%p A008830 a:= n-> numtheory[mlog](n, 2, 11):
%p A008830 seq(a(n), n=1..10);  # _Alois P. Heinz_, Aug 21 2021
%o A008830 (Magma) j := 11; F := FiniteField(j); PrimitiveElement(F); [ Log(F!n) : n in [ 1..j-1 ]];
%o A008830 (Python)
%o A008830 from sympy.ntheory import discrete_log
%o A008830 def a(n): return discrete_log(11, n, 2)
%o A008830 print([a(n) for n in range(1, 11)]) # _Michael S. Branicky_, Aug 13 2021
%Y A008830 Cf. A036117.
%K A008830 nonn,base,fini,full
%O A008830 1,3
%A A008830 _N. J. A. Sloane_