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 A111458 Numbers that cannot be represented as the sum of at most three Fibonacci numbers (with repetitions allowed). 4
 33, 46, 51, 53, 54, 67, 72, 74, 75, 80, 82, 83, 85, 86, 87, 88, 101, 106, 108, 109, 114, 116, 117, 119, 120, 121, 122, 127, 129, 130, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 143, 156, 161, 163, 164, 169, 171, 172 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS R. J. Mathar, Table of n, a(n) for n = 1..1000 EXAMPLE 33 is neither a Fibonacci number nor can be written as the sum of two or three Fibonacci numbers. MAPLE isA111458 := proc(n) # returns true if n is in the sequence local xi, yi, x, y, z ; for xi from 0 do x := A000045(xi) ; if 3*x > n then return true; end if; for yi from xi do y := A000045(yi) ; if x+2*y > n then break; else z := n-x-y ; if isA000045(z) then # see isFib in A000045 return false; end if; end if; end do: end do: end proc: A111458 := proc(n) option remember; local a; if n = 0 then -1; else for a from procname(n-1)+1 do if isA111458(a) then return a; end if; end do: end if; end proc: # R. J. Mathar, Sep 09 2015 MATHEMATICA FibQ[n_] := IntegerQ[Sqrt[5n^2+4]] || IntegerQ[Sqrt[5n^2-4]]; P[n_] := IntegerPartitions[n, 3, Select[Range[n], FibQ]]; Select[Range[1000], P[#] == {}&] (* Jean-François Alcover, Jul 20 2023 *) CROSSREFS Cf. A000045, A000119, A179244, A135709. Sequence in context: A070121 A070122 A247527 * A179244 A258698 A258697 Adjacent sequences: A111455 A111456 A111457 * A111459 A111460 A111461 KEYWORD nonn AUTHOR Stefan Steinerberger, Nov 15 2005 STATUS approved

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Last modified April 12 22:48 EDT 2024. Contains 371639 sequences. (Running on oeis4.)