login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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[3000], BitAnd[#, 2*#] == 0 &], 2, 1];

Position[zeck, 5] // Flatten (* Jean-Fran├žois 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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