cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A065105 Numbers not expressible as a product of Fibonacci numbers.

Original entry on oeis.org

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
Offset: 1

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Author

Joseph L. Pe, Nov 20 2001

Keywords

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.

Examples

			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.
		

Crossrefs

Cf. A000045. Complement of A065108.

Programs

  • 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 *)

Extensions

More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Jan 02 2005
Example corrected by Eric S. Egge, Dec 06 2013