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A008830 Discrete logarithm of n to the base 2 modulo 11. 1
0, 1, 8, 2, 4, 9, 7, 3, 6, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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

REFERENCES

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

LINKS

Table of n, a(n) for n=1..10.

Eric Weisstein's World of Mathematics, Discrete Logarithm.

FORMULA

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

EXAMPLE

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)

MAPLE

a:= n-> numtheory[mlog](n, 2, 11):

seq(a(n), n=1..10);  # Alois P. Heinz, Aug 21 2021

PROG

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

(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

CROSSREFS

Cf. A036117.

Sequence in context: A021552 A245279 A321071 * A248302 A217294 A109614

Adjacent sequences:  A008827 A008828 A008829 * A008831 A008832 A008833

KEYWORD

nonn,base,fini,full

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified May 26 01:44 EDT 2022. Contains 354074 sequences. (Running on oeis4.)