What is the prime Ulam #'s ratio?

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What are Ulam #'s? A ulam #, if an only if it can be written uniquely as the sumof two distinct Ulam #'s. ?

I need to make a list of the firts 20 Ulam #'s. I got the first 8. It's there any formanula or something easy to do it?

How many Ulam number are thre? Prove answer




EXTRA HELP!

Write a program that will generate all Ulam #'s less than a given number n. Use your progam to find all the Ulam numbers less than 1000. I am not good with calculator plus I don't have manual, I have a TI-83.:confused:

How many are there? ?

What portion of these are prime? Prime is a number divisible by one and by itself only... right?
 
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Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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