A214412 - OEIS

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

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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