how to find the smallest taxicab number or Ramanujan number like 1729 larger than N?

I write a .m file to find the a b c d of a taxicab number. The program run well when the num=1729 or some other taxicab number.

But when the num is not a taxicab, the program reture a empty.

I want to know how to find the smallest number large than for example 40000 and find the a b c d

And how to find the first few of taxicab number?

a^3+b^3=c^3+d^3

Your help would be highly appreciated!

clear
format long
num=1729;

b = 1:(num)^(1/3);

a = (num-b.^3).^(1/3);
condition=round(a,10)==round(a,5);
terms = find(condition);
taxicab=round(a(terms));

Answer 1

[David Hill]

There are so few taxicab numbers that you should just use a lookup table.

l=["2", "1729", "87539319", "6963472309248", "48988659276962496", "24153319581254312065344"];

[Daniel Niu]

Thank you, David.

but if I want to 'find' a taxicab. The methods- don't work.

How to find a taxicab number like 87539319?

thank you!

[David Hill]

Bute force

[a,b]=meshgrid(1:500);
t=a.^3+b.^3;
u=unique(t);
h=histc(t(:),u);
f=find(h==6);
min(u(f))

ans = 87539319

[Daniel Niu]

Thank you for your answer，David.