login
Smallest number n with ||n-1||-||n|| = k where ||n||=A005245(n) denotes the complexity of n.
4

%I #18 May 06 2024 10:12:57

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

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

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

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

%H J. Arias de Reyna and J. van de Lune, <a href="http://arxiv.org/abs/1404.1850">The question "How many 1's are needed?" revisited</a>, arXiv preprint arXiv:1404.1850 [math.NT], 2014.

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

%Y Cf. A005245, A252739 (see comments).

%K nonn,more

%O 0,1

%A _Juan Arias-de-Reyna_, Jul 05 2014