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 A179245 Numbers that have 5 terms in their Zeckendorf representation. 11
 88, 122, 135, 140, 142, 143, 177, 190, 195, 197, 198, 211, 216, 218, 219, 224, 226, 227, 229, 230, 231, 266, 279, 284, 286, 287, 300, 305, 307, 308, 313, 315, 316, 318, 319, 320, 334, 339, 341, 342, 347, 349, 350, 352, 353, 354, 360, 362, 363, 365, 366, 367 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A007895(a(n)) = 5. - Reinhard Zumkeller, Mar 10 2013 Numbers that are the sum of five non-consecutive Fibonacci numbers. Their Zeckendorf representation thus consists of five 1's with at least one 0 between each pair of 1's; for example, 122 is represented as 1001010101. - Alonso del Arte, Nov 17 2013 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A048680(A014313(n)). - Charles R Greathouse IV, Nov 17 2013 EXAMPLE 88  = 55 + 21 + 8 + 3 + 1. 122 = 89 + 21 + 8 + 3 + 1. 135 = 89 + 34 + 8 + 3 + 1. 140 = 89 + 34 + 13 + 3 + 1. 142 = 89 + 34 + 13 + 5 + 1. 81 is not in the sequence because, although it is the sum of five Fibonacci numbers (81 = 5 + 8 + 13 + 21 + 34), its Zeckendorf representation only has three terms: 81 = 55 + 21 + 5. MAPLE with(combinat): B := proc (n) local A, ct, m, j: A := proc (n) local i: for i while fibonacci(i) <= n do n-fibonacci(i) end do end proc: ct := 0: m := n: for j while 0 < A(m) do ct := ct+1: m := A(m) end do: ct+1 end proc: Q := {}: for i from fibonacci(11)-1 to 400 do if B(i) = 5 then Q := `union`(Q, {i}) else end if end do: Q; MATHEMATICA zeck = DigitCount[Select[Range, BitAnd[#, 2*#] == 0 &], 2, 1]; Position[zeck, 5] // Flatten (* Jean-François Alcover, Jan 30 2018 *) PROG (Haskell) a179245 n = a179245_list !! (n-1) a179245_list = filter ((== 5) . a007895) [1..] -- Reinhard Zumkeller, Mar 10 2013 (PARI) A048680(n)=my(k=1, s); while(n, if(n%2, s+=fibonacci(k++)); k++; n>>=1); s [A048680(n)|n<-[1..100], hammingweight(n)==5] \\ Charles R Greathouse IV, Nov 17 2013 CROSSREFS Cf. A035517, A007895. Numbers that have m terms in their Zeckendorf representations: A179242 (m = 2), A179243 (m = 3), A179244 (m = 4), A179246 (m = 6), A179247 (m = 7), A179248 (m = 8), A179249 (m = 9), A179250 (m = 10), A179251 (m = 11), A179252 (m = 12), A179253 (m = 13). Sequence in context: A183186 A161194 A196581 * A174651 A225136 A039445 Adjacent sequences:  A179242 A179243 A179244 * A179246 A179247 A179248 KEYWORD nonn,easy AUTHOR Emeric Deutsch, Jul 05 2010 STATUS approved

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Last modified July 25 16:39 EDT 2021. Contains 346291 sequences. (Running on oeis4.)