A072540 Numbers that are not differences between successive Ulam numbers (A002858).

6, 11, 14, 16, 18, 21

Offset: 1

Author

Benoit Cloitre, Aug 04 2002

Keywords

• more
• nonn
• hard

Comments

Unfortunately, it appears that the entries are all conjectural. I am not aware of any proofs that the listed numbers can never appear. The terms shown are those listed by Pickover. - N. J. A. Sloane, Jun 19 2008

However, a gap of 35 doesn't occur until after the 35755308th term (483379914), so these missing gaps could eventually occur. - Jud McCranie, Jun 13 2008

The sequence is conjectured to continue: 23, 26, 28, 31, 33. These gaps do not appear in the first 158000000 terms, so are candidates for the sequence. [Jud McCranie, Sep 12 2013]

The conjectured list of gaps that don't appear holds through the first 28 billion Ulam numbers. - Jud McCranie, Jan 07 2016

References

• Clifford A. Pickover, "Wonders of Numbers, ...", Oxford University Press, 2000

Links

• Philip Gibbs and Judson McCranie, The Ulam Numbers up to One Trillion, (2017).
• Shyam Sunder Gupta, Ulam Numbers. In: Exploring the Beauty of Fascinating Numbers. Springer Praxis Books(). Springer, Singapore, (2025).
• C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Zentralblatt review

Crossrefs

Cf. A002858, A072832.

Extensions

Edited by Max Alekseyev, Dec 19 2011