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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 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 STATUS approved

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