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A008831 Discrete logarithm of n to the base 2 modulo 13. 2
0, 1, 4, 2, 9, 5, 11, 3, 8, 10, 7, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
This is also a (12,1)-sequence.
Equivalently, a(n) is the multiplicative order of n with respect to base 2 (modulo 13), i.e., a(n) is the base-2 logarithm of the smallest k such that 2^k mod 13 = n.
REFERENCES
I. M. Vinogradov, Elements of Number Theory, p. 220.
LINKS
H. Y. Song and S. W. Golomb, Generalized Welch-Costas sequences and their application to Vatican arrays, in Proc. 2nd International Conference on Finite Fields: Theory, Algorithms and Applications (Las Vegas 1993) Contemp. Math. vol. 168 344 1994.
Eric Weisstein's World of Mathematics, Discrete Logarithm.
FORMULA
2^a(n) == n (mod 13). - Michael S. Branicky, Aug 22 2021
EXAMPLE
From Jon E. Schoenfield, Aug 21 2021: (Start)
Sequence is a permutation of the 12 integers 0..11:
k 2^k 2^k mod 13
-- ------ ----------
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 3 so a(3) = 4
5 32 6 so a(6) = 5
6 64 12 so a(12) = 6
7 128 11 so a(11) = 7
8 256 9 so a(9) = 8
9 512 5 so a(5) = 9
10 1024 10 so a(10) = 10
11 2048 7 so a(7) = 11
12 4096 1
but a(1) = 0, so the sequence is finite with 12 terms.
(End)
MAPLE
[ seq(numtheory[mlog](n, 2, 13), n=1..12) ];
MATHEMATICA
a[1] = 0; a[n_] := MultiplicativeOrder[2, 13, {n}]; Array[a, 12] (* Jean-François Alcover, Feb 09 2018 *)
PROG
(Python)
from sympy.ntheory import discrete_log
def a(n): return discrete_log(13, n, 2)
print([a(n) for n in range(1, 13)]) # Michael S. Branicky, Aug 22 2021
CROSSREFS
A row of A054503.
Sequence in context: A163253 A191663 A206561 * A365378 A289506 A363268
KEYWORD
nonn,base,fini,full
AUTHOR
STATUS
approved

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)