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A008830
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Discrete logarithm of n to the base 2 modulo 11.
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1
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OFFSET
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1,3
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COMMENTS
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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
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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 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)
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MAPLE
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a:= n-> numtheory[mlog](n, 2, 11):
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn,base,fini,full
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AUTHOR
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STATUS
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approved
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