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A065105 Numbers not expressible as a product of Fibonacci numbers. 2
7, 11, 14, 17, 19, 22, 23, 28, 29, 31, 33, 35, 37, 38, 41, 43, 44, 46, 47, 49, 51, 53, 56, 57, 58, 59, 61, 62, 66, 67, 69, 70, 71, 73, 74, 76, 77, 79, 82, 83, 85, 86, 87, 88, 91, 92, 93, 94, 95, 97, 98, 99, 101, 103, 106, 107, 109, 111, 112, 113, 114, 115, 116, 118, 119, 121 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

I conjecture that for this sequence, a(n + 1) - a(n) <= 5 for all n; and a(n + 1) - a(n) <= 3 for n >= 8.

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

28 = 2*14 = 4*7 is a term in the sequence because 28, 14, and 7 are not Fibonacci numbers. 63 = 3*21 is not a term in the sequence because 3 and 21 are Fibonacci numbers.

MAPLE

with(combinat): A000045:=proc(n) options remember: RETURN(fibonacci(n)): end: mulfib:=proc(m, i) local j, q, f: f:=0: for j from i by -1 to 3 while(f=0) do if(irem(m, A000045(j))=0) then q:=iquo(m, A000045(j)): if(q=1) then RETURN(1) else f:=mulfib(q, j) fi fi od: RETURN(f): end: for i from 3 to 11 do for n from A000045(i) to A000045(i+1)-1 do m:=mulfib(n, i): if m=0 then printf("%d, ", n) fi od od: # C. Ronaldo

MATHEMATICA

f[lst_] := Take[ Union[ Flatten[ Table[ lst[[i]]lst[[j]], {i, Length[lst]}, {j, i}]]], 70]; Complement[ Range[189], Nest[f, Fibonacci[Range[2, 20]], 3]] (* Robert G. Wilson v, Feb 12 2005 *)

CROSSREFS

Cf. A000045. Complement of A065108.

Sequence in context: A004235 A004236 A153049 * A118797 A080837 A168135

Adjacent sequences:  A065102 A065103 A065104 * A065106 A065107 A065108

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Nov 20 2001

EXTENSIONS

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 02 2005

Example corrected by Eric S. Egge, Dec 06 2013

STATUS

approved

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Last modified September 18 20:22 EDT 2019. Contains 327181 sequences. (Running on oeis4.)