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A010684
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Period 2: repeat (1,3); offset 0.
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52
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1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1
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OFFSET
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0,2
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COMMENTS
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Hankel transform is [1,-8,0,0,0,0,0,0,0,0,...]. - Philippe Deléham, Mar 29 2007
Continued fraction expansion of (3+sqrt(21))/6. - Klaus Brockhaus, May 04 2010
Positive sum of the coordinates from the image of the point (1,-2) after n 90-degree rotations about the origin. - Wesley Ivan Hurt, Jul 06 2013
This sequence can be generated by an infinite number of formulas having the form a^(b*n) mod c where a is congruent to 3 mod 4 and b is any odd number. If a is congruent to 3 mod 4 then c can be 4; if a is also congruent to 3 mod 8 then c can be 8. For example: a(n)= 15^(3*n) mod 4, a(n) = 19^(5*n) mod 4, a(n) = 19^(5*n) mod 8. - Gary Detlefs, May 19 2014
This sequence is also the unsigned periodic Schick sequence for p = 5. See the Schick reference, p. 158, for p = 5.- Wolfdieter Lang, Apr 03 2020
Digits following the decimal point when 1/3 is converted to base 5. - Jamie Robert Creasey, Oct 15 2021
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REFERENCES
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Carl Schick, Trigonometrie und unterhaltsame Zahlentheorie, Bokos Druck, Zürich, 2003 (ISBN 3-9522917-0-6). Tables 3.1 to 3.10, for odd p = 3..113 (with gaps), pp. 158-166.
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LINKS
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FORMULA
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a(n) = 2-(-1)^n.
G.f.: (1+3x)/((1-x)(1+x)).
E.g.f.: 2*exp(x) - exp(-x). (End)
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MAPLE
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MATHEMATICA
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PROG
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(Sage) [power_mod(3, n, 8)for n in range(0, 81)] # Zerinvary Lajos, Nov 24 2009
(Python)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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