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A002266
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Integers repeated 5 times.
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52
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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
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OFFSET
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0,11
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COMMENTS
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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
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)
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LINKS
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FORMULA
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a(n) = floor(n/5), n >= 0.
G.f.: x^5/((1-x)(1-x^5)).
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
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MAPLE
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MATHEMATICA
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Table[{n, n, n, n, n}, {n, 0, 20}]//Flatten (* Harvey P. Dale, Jun 17 2022 *)
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PROG
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(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
(Python)
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CROSSREFS
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Cf. A002162, A008648, A004526, A002264, A002265, A010761, A010762, A110532, A110533, A010872, A010873, A010874.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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