PARI/GP, 76 73 bytes

Saved three bytes courtesy of Mitch Schwartz.

for(n=b=!a=1,99,b=a+a=b;print(if(b%2,"",Fibo)if(b%3,if(b%2,b,""),Nacci)))

Sample Usage

$ gp -qf < fibo-nacci.gp

PARI/GP, 76 73 bytes

Saved three bytes courtesy of Mitch Schwartz.

for(n=b=!a=1,99,b=a+a=b;print(if(b%2,"",Fibo)if(b%3,if(b%2,b,""),Nacci)))

Sample Usage

$ gp -qf < fibo-nacci.gp

PARI/GP, 73 bytes

for(n=b=!a=1,99,b=a+a=b;print(if(b%2,"",Fibo)if(b%3,if(b%2,b,""),Nacci)))

Sample Usage

$ gp -qf < fibo-nacci.gp

PARI/GP, 76 73 bytes

Saved three bytes courtesy of Mitch Schwartz.

for(n=b=!a=1,99,b=a+a=b;print(if(b%2,"",Fibo)if(b%3,if(b%2,b,""),Nacci)))

Sample Usage

$ gp -qf < fibo-nacci.gp

PARI/GP, 76 bytes

for(n=1,100,f=fibonacci(n);print(if(f%2,"",Fibo)if(f%3,if(f%2,f,""),Nacci)))

Sample Usage

$ gp -qf < fibo-nacci.gp

PARI/GP, 73 bytes

for(n=b=!a=1,99,b=a+a=b;print(if(b%2,"",Fibo)if(b%3,if(b%2,b,""),Nacci)))

Sample Usage

$ gp -qf < fibo-nacci.gp