# [seqfan] Sequence of paired terms

David Sycamore djsycamore at yahoo.co.uk
Thu May 14 17:41:53 CEST 2020

```﻿Hi,
>
> The following sequence consists of paired terms: (a(2*k+1), a(2*k+2)); in which, for each k>=0,  if we modify the pair by moving the comma I digit place, from between the terms to between the first two digits of the second term, then we find that the sum of the original pair and the sum of the modified pair are the same. Eg. 1,10=>sum=11; 11,0=>sum=11. No number can appear more than once in the same position within any pair, and the idea is for a lexico least form of this sequence, starting a(1)=1; thus:
>
> 1,10,1,11,1,12......1,19,
> 2,20,2,21,..........2,29,
> 3,30,3,31,  .........3,39,
> ..
> ..
> ..
>
> 9,90,9,91,...................9,99,
11,101,11,102,11,103,....11,199
>
> I’m not sure how it goes after that; perhaps: 111,1000,111,1001,111,1002,...............111,1999
> etc..
>
> I would appreciate to have some confirmation of these (hand made) terms, plus any comments. It might also be interesting to see what the plots look like.
> Best regards
> David.

```