# [seqfan] Re: An arithmetic conjecture

Peter Luschny peter.luschny at googlemail.com
Wed Mar 18 13:45:18 CET 2009

```> Start M[1] = 1, K[1] = 0. For given m > 1
> let s(m) denote the smallest k such that
> the conjecture holds - assuming existence -
> or 0 if not. Further let t(m) be the maximum
> of the s(i) for all i <= m.
> Now list those pairs m,t(m) where t(m) increases.

RG> Your sequence has errors,

Yes, I know (in the meantime). There are
two omissions. Originally I took the list
from the postings of the de.sci.math thread.
In the meantime I have recomputed the list
by myself.

RG> here it is a correction and extension of the
RG> sequence:

M K
1 0
5 2
8 3
19 5
21 12
27 15
49 21
110 29
118 34
165 58
2769 61
2837 65
3661 70
14354 74
59913 103
1786453 112
2702893 117
2712849 121
7384247 122
21219075 130
193702717 153
899019601 156
1305797743 159

This agrees with my list. Thank you Robert
for checking. The list continues:

8155079481 168
9856426495 169
15164102636 170
28051390987 177

The corrected and extended list is displayed
for more than a week now on

http://www.luschny.de/math/vermutung.html

Cheers Peter

```