|
Search: id:A065105
|
|
|
| A065105 |
|
Numbers not expressible as a product of Fibonacci numbers. |
|
+0
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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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.
|
|
EXAMPLE
|
63 = 3^2 * 7 is not expressible as a product of Fibonacci numbers since 7 is not.
|
|
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]] (from Robert G. Wilson v Feb 12 2005)
|
|
CROSSREFS
|
Cf. A000045. Complement of A065108.
Adjacent sequences: A065102 A065103 A065104 this_sequence A065106 A065107 A065108
Sequence in context: A045970 A004235 A004236 this_sequence A118797 A080837 A120687
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Nov 20 2001
|
|
EXTENSIONS
|
More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 02 2005
|
|
|
Search completed in 0.002 seconds
|
