MATLAB: Fibonacci sequence up to first 256 elements

fibbonacci long sequence

I want to generate first 256 fibonacci sequence elments . the code is repeating a fixed number after some terms, I think that we can use maximum of uint 64 and if a number gets begger we just stuck or is there any other reason or mistake in the code.
clear
format long g
n(1) =uint64(1);
n(2) = 1;
k = 3;
while k <= 256
    n(k) = [n(k-2) + n(k-1)];
    k = k + 1;
end
ff=mod(n,256);
%fprintf('%g,',n)
what I m getting is
Columns 91 through 105
    69   189     2   255   255   255   255   255   255   255   255   255   255   255   255
  Columns 106 through 120
   255   255   255   255   255   255   255   255   255   255   255   255   255   255   255
  Columns 121 through 135

Best Answer

While this is surely homework, you got it almost correct, with a few major errors.
  1. Preallocate the vector!!!!!!!!!!!!!! Never grow an array dynamically, as otherwise, your next anguished question will be to ask why is my code so slow!
  2. Recognize that the modulus operation can be done inside the loop! This applies to the identity:
mod(a+b,P) = mod(mod(a,P) + mod(b,P),P)
Why is that important? Because you will never need to overflow. Your code can now become:
n = zeros(1,256);
n(1:2) = 1;
for k=3:256
  n(k) = mod(n(k-2) + n(k-1),256);
end
fprintf('%g,',n)
As you see, there is no need to use uint64 either. Double precision is entirely adequate. In fact uint16 or int16 would have been entirely adequate.
1,1,2,3,5,8,13,21,34,55,89,144,233,121,98,219,61,24,85,109,194,47,241,32,17,49,66,115,181,40,221,5,226,231,201,176,121,41,162,203,109,56,165,221,130,95,225,64,33,97,130,227,101,72,173,245,162,151,57,208,9,217,226,187,157,88,245,77,66,143,209,96,49,145,194,83,21,104,125,229,98,71,169,240,153,137,34,171,205,120,69,189,2,191,193,128,65,193,2,195,197,136,77,213,34,247,25,16,41,57,98,155,253,152,149,45,194,239,177,160,81,241,66,51,117,168,29,197,226,167,137,48,185,233,162,139,45,184,229,157,130,31,161,192,97,33,130,163,37,200,237,181,162,87,249,80,73,153,226,123,93,216,53,13,66,79,145,224,113,81,194,19,213,232,189,165,98,7,105,112,217,73,34,107,141,248,133,125,2,127,129,0,129,129,2,131,133,8,141,149,34,183,217,144,105,249,98,91,189,24,213,237,194,175,113,32,145,177,66,243,53,40,93,133,226,103,73,176,249,169,162,75,237,56,37,93,130,223,97,64,161,225,130,99,229,72,45,117,162,23,185,208,137,89,226,59
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