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%I #24 Feb 13 2021 01:09:17
%S 88,122,135,140,142,143,177,190,195,197,198,211,216,218,219,224,226,
%T 227,229,230,231,266,279,284,286,287,300,305,307,308,313,315,316,318,
%U 319,320,334,339,341,342,347,349,350,352,353,354,360,362,363,365,366,367
%N Numbers that have 5 terms in their Zeckendorf representation.
%C A007895(a(n)) = 5. - _Reinhard Zumkeller_, Mar 10 2013
%C 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
%H Reinhard Zumkeller, <a href="/A179245/b179245.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A048680(A014313(n)). - _Charles R Greathouse IV_, Nov 17 2013
%e 88 = 55 + 21 + 8 + 3 + 1.
%e 122 = 89 + 21 + 8 + 3 + 1.
%e 135 = 89 + 34 + 8 + 3 + 1.
%e 140 = 89 + 34 + 13 + 3 + 1.
%e 142 = 89 + 34 + 13 + 5 + 1.
%e 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.
%p 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;
%t zeck = DigitCount[Select[Range[3000], BitAnd[#, 2*#] == 0 &], 2, 1];
%t Position[zeck, 5] // Flatten (* _Jean-François Alcover_, Jan 30 2018 *)
%o (Haskell)
%o a179245 n = a179245_list !! (n-1)
%o a179245_list = filter ((== 5) . a007895) [1..]
%o -- _Reinhard Zumkeller_, Mar 10 2013
%o (PARI) A048680(n)=my(k=1,s);while(n,if(n%2,s+=fibonacci(k++)); k++; n>>=1); s
%o [A048680(n)|n<-[1..100],hammingweight(n)==5] \\ _Charles R Greathouse IV_, Nov 17 2013
%Y 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).
%K nonn,easy
%O 1,1
%A _Emeric Deutsch_, Jul 05 2010
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