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

1,2

Comments

0 is considered to be a Fibonacci number.

Links

Table of n, a(n) for n=1..60.

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 *)

Prog

(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,

Crossrefs

Cf. A000045, A132144, A214410.

Sequence in context: A252458 A271720 A243436 * A080361 A054295 A328241

Adjacent sequences: A214409 A214410 A214411 * A214413 A214414 A214415

Keyword

nonn,easy

Author

Alex Ratushnyak, Jul 16 2012

Status

approved