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A008831
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Discrete logarithm of n to the base 2 modulo 13.
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2
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0, 1, 4, 2, 9, 5, 11, 3, 8, 10, 7, 6
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OFFSET
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1,3
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COMMENTS
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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.
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REFERENCES
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I. M. Vinogradov, Elements of Number Theory, p. 220.
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LINKS
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FORMULA
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EXAMPLE
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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)
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MAPLE
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[ seq(numtheory[mlog](n, 2, 13), n=1..12) ];
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MATHEMATICA
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a[1] = 0; a[n_] := MultiplicativeOrder[2, 13, {n}]; Array[a, 12] (* Jean-François Alcover, Feb 09 2018 *)
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PROG
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(Python)
from sympy.ntheory import discrete_log
def a(n): return discrete_log(13, n, 2)
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CROSSREFS
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KEYWORD
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nonn,base,fini,full,changed
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AUTHOR
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STATUS
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approved
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