Determine the first digit of each element of Fibonacci Sequence.

Using your favorite programing language (Matlab) compute the first 1000 elements of the Fibonacci sequence f(n) =f(n−1) +f(n−2) where f(1) = f(2) = 1. Determine the first digit of each element .

Here, I can find the 1000 element easily using the Fibonacci function. But I am not sure how to the get the first digit of the fist 1000 element. Any suggestion will be appriciated. Thanks

[Walter Roberson]

How are you going to find the 1000 terms? The 1000th Fibonacci has over 2000 digits. If you proceed with double precision, you will get some number, but can you be sure that the leading digits would be right considering the loss of precision?

[mouaz chowdhury]

I was thinking about doing this.

n = 1: 1000;

fibonacci(n);

Shouldnt this work?

[Walter Roberson]

You can use 1o^floor(log10(x)) to get a number between 1 and (10-eps) ...

Answer 1

[David Hill]

str2double(cellfun(@(x)x(1),arrayfun(@(x)num2str(x),fibonacci(1:1000),'UniformOutput',false),'UniformOutput',false));

I think the above provides you with an array of the first digits of the fibonacci numbers up to 1000.

[Rik]

suggested=str2double(cellfun(@(x)x(1),arrayfun(@(x)num2str(x),fibonacci(1:1000),'UniformOutput',false),'UniformOutput',false));

fib=zeros(1,1000);
fib(1:2)=1;
out=fib;
for n=3:1000
    fib(n)=fib(n-1)+fib(n-2);
    tmp=sprintf('%.5e',fib(n));
    out(n)=tmp(1)-'0';
end

if any(out-suggested)
    disp('at least one method is wrong')
else
    disp('both are correct, or wrong in the same places')
end

There is no checking for potential issues like Walter suggests, but is seems the symbolic toolbox handles it well enough. Or both have an error in the same place.

[Walter Roberson]

Futher testing with symbolic calculations shows that using numeric approximation to double gives the same first digit as for exact calculations.