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
Links
- David Radcliffe, Table of n, a(n) for n = 1..1000
Programs
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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=', ')
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