A214412 Numbers that can't be expressed as the sum of a Fibonacci number and a square of a positive integer.

0, 8, 13, 15, 20, 23, 31, 32, 34, 40, 42, 45, 47, 48, 53, 55, 58, 60, 61, 63, 68, 73, 74, 75, 76, 78, 79, 87, 88, 92, 95, 96, 97, 99, 106, 107, 109, 110, 111, 112, 116, 117, 118, 120, 127, 128, 130, 131, 132, 133, 135, 137, 139, 140, 141, 143, 150, 151, 154, 156

Offset: 1

Author

Alex Ratushnyak, Jul 16 2012

Keywords

• nonn
• easy

Comments

0 is considered to be a Fibonacci number.

Links

• David Radcliffe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000045, A132144, A214410.

Programs

Maple

q:= proc(n) local f,g; f,g:= 0,1;
      do if f>=n       then return true
       elif issqr(n-f) then return false
       else f,g:= g,f+g
      fi od
    end:
select(q, [$0..200])[];  # Alois P. Heinz, May 22 2021

Mathematica

nn = 156; sq = Range[Sqrt[nn]]^2; fb = {}; i = 0; While[f = Fibonacci[i];  f < nn, i++; AppendTo[fb, f]]; fb = Union[fb]; Complement[Range[0, nn], Union[Flatten[Outer[Plus, sq, fb]]]] (* T. D. Noe, Jul 31 2012 *)

Python

prpr = 0
prev = 1
fib = [0]*100
for n in range(100):
    fib[n] = prpr
    curr = prpr+prev
    prpr = prev
    prev = curr
#print fib[n]
for n in range(777):
    i = 1
    yes = 0
    while i*i<=n:
        r = n - i*i
        if r in fib:
            yes = 1
            break
        i += 1
    if yes==0:
        print(n, end=', ')