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%I #13 Aug 11 2017 20:45:48
%S 7,11,14,17,19,22,23,28,29,31,33,35,37,38,41,43,44,46,47,49,51,53,56,
%T 57,58,59,61,62,66,67,69,70,71,73,74,76,77,79,82,83,85,86,87,88,91,92,
%U 93,94,95,97,98,99,101,103,106,107,109,111,112,113,114,115,116,118,119,121
%N Numbers not expressible as a product of Fibonacci numbers.
%C 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.
%e 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.
%p 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
%t 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 *)
%Y Cf. A000045. Complement of A065108.
%K nonn
%O 1,1
%A _Joseph L. Pe_, Nov 20 2001
%E More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 02 2005
%E Example corrected by _Eric S. Egge_, Dec 06 2013
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