A244743 Smallest number n with ||n-1||-||n|| = k where ||n||=A005245(n) denotes the complexity of n.

6, 12, 24, 108, 720, 1440, 81648, 2041200, 612360000

Offset: 0

Author

Juan Arias-de-Reyna, Jul 05 2014

Keywords

• nonn
• more

Comments

The k-th term of this sequence is the least n with ||n-1||-||n|| = k if such an n exists.

It is conjectured that ||n-1||-||n|| is not bounded. But there is no proof that the sequence is infinite or is well defined.

Examples

			||719||=23, ||720||=19, therefore ||719||-||720||=4. This is the first time the difference 4 appears in this way. Hence a(4)=720.
		

Links

• J. Arias de Reyna and J. van de Lune, The question "How many 1's are needed?" revisited, arXiv preprint arXiv:1404.1850 [math.NT], 2014.

Crossrefs

Cf. A005245, A252739 (see comments).