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A010684 Period 2: repeat (1,3); offset 0. 52
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Hankel transform is [1,-8,0,0,0,0,0,0,0,0,...]. - Philippe Deléham, Mar 29 2007
Binomial transform gives [1,4,8,16,32,64,...] (A151821(n+1)). - Philippe Deléham, Sep 17 2009
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
REFERENCES
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.
LINKS
FORMULA
From Paul Barry, Apr 29 2003: (Start)
a(n) = 2-(-1)^n.
G.f.: (1+3x)/((1-x)(1+x)).
E.g.f.: 2*exp(x) - exp(-x). (End)
a(n) = 2*A153643(n) - A153643(n+1). - Paul Curtz, Dec 30 2008
a(n) = 3^(n mod 2). - Jaume Oliver Lafont, Mar 27 2009
a(n) = 7^n mod 4. - Vincenzo Librandi, Feb 07 2011
a(n) = 1 + 2*(n mod 2). - Wesley Ivan Hurt, Jul 06 2013
a(n) = A000034(n) + A000035(n). - James Spahlinger, Feb 14 2016
MAPLE
[seq (modp((2*n+1), 4), n=0..80)]; # Zerinvary Lajos, Nov 30 2006
MATHEMATICA
Table[2-(-1)^n, {n, 0, 100}] (* Wesley Ivan Hurt, Mar 24 2014 *)
PROG
(Sage) [power_mod(3, n, 8)for n in range(0, 81)] # Zerinvary Lajos, Nov 24 2009
(PARI) a(n)=1+n%2*2 \\ Charles R Greathouse IV, Dec 28 2011
(Python)
def A010684(n): return 3 if n&1 else 1 # Chai Wah Wu, Jan 17 2023
CROSSREFS
Cf. A112030, A112033, A176014 (decimal expansion of (3+sqrt(21))/6).
Sequence in context: A066056 A153284 A112030 * A176040 A125768 A334949
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)