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 A002266 Integers repeated 5 times. 48
 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 COMMENTS For n > 3, number of consecutive "11's" after the (n+3) "1's" in the continued fraction for sqrt(L(n+2)/L(n)) where L(n) is the n-th Lucas number A000032 (see example). E.g., the continued fraction for sqrt(L(11)/L(9)) is [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 11, 58, 2, 4, 1, ...] with 12 consecutive ones followed by floor(11/5)=2 elevens. - Benoit Cloitre, Jan 08 2006 Complement of A010874, since A010874(n) + 5*a(n) = n. - Hieronymus Fischer, Jun 01 2007 From Paul Curtz, May 13 2020: (Start) Main N-S vertical of the pentagonal spiral built with this sequence is A001105:                               21                           20  15  15                       20  14  10  10  15                   20  14   9   6   6  10  15               20  14   9   5   3   3   6  10  15           20  14   9   5   2   1   1   3   6  10  16       19  14   9   5   2   0   0   0   1   3   6  11  16         19   13   9   5  2   0   0    1   3   7 11  16           19  13    8  5   2   2   1   4   7  11  16             19   13   8  4   4   4   4   7  11  16               19  13   8   8   8   7   7  11  17                  18  13  12 12  12  12  12  17                    18  18 18  18  17  17  17 The main S-N vertical and the next one are A000217. (End) LINKS Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1). FORMULA a(n) = floor(n/5), n >= 0. G.f.: x^5/((1-x)(1-x^5)). a(n) = -1 + Sum_{k=0..n} ((8*(sin(2*Pi*k/5))^2-5)^2-5)/20, with n>=0. a(n)= -1 + Sum_{k=0..n} (1/50)*(-9*(k mod 5) + ((n+1) mod 5) + ((n+2) mod 5) + ((n+3) mod 5) + 11*((n+4) mod 5)), with n >= 0. - Paolo P. Lava, May 15 2007 a(n) = (n - A010874(n))/5. - Hieronymus Fischer, May 29 2007 Also, floor((n^5-1)/5*n^4) will produce this sequence. Moreover, floor((n^5-n^4)/(5*n^4-4*n^3)) (n >= 1) will produce this sequence as well. - Mohammad K. Azarian, Nov 08 2007 For n >= 5, a(n) = floor(log_5(5^a(n-1) + 5^a(n-2) + 5^a(n-3) + 5^a(n-4) + 5^a(n-5))). - Vladimir Shevelev, Jun 22 2010 MAPLE A002266:=n->floor(n/5); seq(A002266(n), n=0..100); # Wesley Ivan Hurt, Dec 10 2013 MATHEMATICA Table[Floor[n/5], {n, 0, 20}] (* Wesley Ivan Hurt, Dec 10 2013 *) Table[{n, n, n, n, n}, {n, 0, 20}]//Flatten (* Harvey P. Dale, Jun 17 2022 *) PROG (Sage) [floor(n/5) - 1 for n in range(5, 88)] # Zerinvary Lajos, Dec 01 2009 (Haskell) a002266 = (`div` 5) a002266_list = [0, 0, 0, 0, 0] ++ map (+ 1) a002266_list -- Reinhard Zumkeller, Nov 27 2012 (PARI) a(n)=n\5 \\ Charles R Greathouse IV, Dec 10 2013 CROSSREFS a(n) = A010766(n, 5). Cf. A008648, A004526, A002264, A002265, A010761, A010762, A110532, A110533, A010872, A010873, A010874. Partial sums: A130520. Sequence in context: A092278 A105512 A301506 * A075249 A008648 A154099 Adjacent sequences:  A002263 A002264 A002265 * A002267 A002268 A002269 KEYWORD nonn,easy AUTHOR EXTENSIONS Incorrect formula removed by Ridouane Oudra, Oct 16 2021 STATUS approved

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Last modified July 3 17:50 EDT 2022. Contains 355055 sequences. (Running on oeis4.)