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 A010684 Period 2: repeat (1,3); offset 0. 49
 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 Index entries for linear recurrences with constant coefficients, signature (0,1). 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) = 3*(n mod 2) + (n+1) mod 2. - Paolo P. Lava, Oct 20 2006 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 CROSSREFS Cf. A112030, A112033, A176014 (decimal expansion of (3+sqrt(21))/6). Sequence in context: A066056 A153284 A112030 * A176040 A125768 A334949 Adjacent sequences:  A010681 A010682 A010683 * A010685 A010686 A010687 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified September 28 02:47 EDT 2022. Contains 357063 sequences. (Running on oeis4.)