perplexus.info :: Numbers : Ulam numbers

Ulam numbers (Posted on 2017-06-03)

We define recursively the Ulam numbers by setting u1 = 1, u2 = 2, and for each subsequent integer n, we set n equal to the next Ulam number if it can be written uniquely as the sum of two different Ulam numbers; e.g.: u3 = 3, u4 = 4, u5 = 6, etc.

Prove that there are infinitely many Ulam numbers.

Now a D4 BONUS.
3 (=1+2). Find another Ulam number is that is the sum of two consecutive Ulam numbers.

How about a 3rd one?

Submitted by Ady TZIDON

Rating: 3.0000 (1 votes)

Solution: (Hide)

3 (=1+2) and 131 (=62+69) are the only two Ulam numbers known so far that constitute a sum of two consecutive Ulam numbers.
In the first 28 billion Ulam numbers there are no others possessing this feature.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
What the OEIS says	Brian Smith	2017-06-04 09:42:56
One erratum and one ENCORE	Ady TZIDON	2017-06-04 08:10:31
re: The proof and the bonus	Charlie	2017-06-03 14:34:24
The proof and the bonus	Charlie	2017-06-03 14:31:38
Proof (spoiler)	Steve Herman	2017-06-03 08:33:53

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