Review: A048859

[Dean Hickerson]

David Wilson asked:

> Is anyone able to relate the values of A048859 to the formula?

Here are the values and 'formula':

%S A048859 1,2,4,7,9,14,20,25,31,34,44
%F A048859 Keep first k numbers, skip the k+1 numbers, for k=2,3,4,...

Since so few terms are given, it seems likely that they were computed by
hand, and maybe the author miscomputed.  Consider the following interpretation
of the formula:  Start with the sequence of positive integers.  Delete
every 3rd term, then delete every 4th term of what's left, then delete every
5th term, ...  We get:

%S A000000 1,2,4,7,10,14,20,25,32,40,46,55,67,74,91,104,112,127,145,154,175,194,
%T A000000 200,230,241,265,284,307,325,355,382,404,422,464,475,505,547,556,595,
%U A000000 631,661,680,736,742,790,847,860,904,950,967,1012,1081,1094,1135,1184

%t A000000 del[lst_,k_]:=lst[[Select[Range[Length[lst]],Mod[#,k]!=0&]]]; For[k=3;s=Range[1000],k<=Length[s],k++,s=del[s,k]]; s

Perhaps the author made 2 mistakes:  He wrote 9 instead of 10, and he skipped
the step in which every 9th term is deleted.  After deleting every 3rd term,
..., every 8th term, we get:

    1 2 4 7 10 14 20 25 31 32 34 40 44

Then deleting the 10th term gets rid of 32 and deleting the 11th remaining
term gets rid of 40, leaving:

    1 2 4 7 10 14 20 25 31 34 44

which agrees with the original sequence except for the 10.


Note that if we instead start by deleting every 2nd term, we get A000960.

Dean Hickerson
dean at math.ucdavis.edu