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

0, 1, 8, 2, 4, 9, 7, 3, 6, 5

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• fini
• full

Comments

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

Examples

			From _Jon E. Schoenfield_, Aug 21 2021: (Start)
Sequence is a permutation of the 10 integers 0..9:
   k     2^k  2^k mod 11
  --  ------  ----------
   0       1           1  so a(1)  =  0
   1       2           2  so a(2)  =  1
   2       4           4  so a(4)  =  2
   3       8           8  so a(8)  =  3
   4      16           5  so a(5)  =  4
   5      32          10  so a(10) =  5
   6      64           9  so a(9)  =  6
   7     128           7  so a(7)  =  7
   8     256           3  so a(3)  =  8
   9     512           6  so a(6)  =  9
  10    1024           1
but a(1) = 0, so the sequence is finite with 10 terms.
(End)
		

References

• I. M. Vinogradov, Elements of Number Theory, p. 220.

Links

• Eric Weisstein's World of Mathematics, Discrete Logarithm.

Crossrefs

Cf. A036117.

Programs

Magma

j := 11; F := FiniteField(j); PrimitiveElement(F); [ Log(F!n) : n in [ 1..j-1 ]];

Maple

a:= n-> numtheory[mlog](n, 2, 11):
seq(a(n), n=1..10);  # Alois P. Heinz, Aug 21 2021

Python

from sympy.ntheory import discrete_log
def a(n): return discrete_log(11, n, 2)
print([a(n) for n in range(1, 11)]) # Michael S. Branicky, Aug 13 2021

Formula

2^a(n) == n (mod 11). - Michael S. Branicky, Aug 13 2021