# [seqfan] Re: Incongruous reordering of N

N. J. A. Sloane njas at research.att.com
Mon Nov 2 01:54:51 CET 2009

```Eric suggested:
Here is an incongruous reordering of the Naturals;
1) start S with 1,2,3
2) to get the next term, simply add the last two terms;
3) look back at S and call T the smallest natural num-
ber not present in S;
4) let T become the last term of S;
5) goto (2)
Seq S starts:
1,2,3,5,4,9,6,15,7,22,8,30,10,40,11,51,12,73,13,86,14,100,...

Superseeker hints that perhaps the following is what was intended!

%I A022941
%S A022941 1,2,5,9,15,22,30,40,51,63,76,90,106,123,141,160,180,201,224,248,
%T A022941 273,299,326,354,383,414,479,513,548,584,621,659,698,739,781,824,
%U A022941 868,913,959,1006,1054,1103,1153,1205,1258,1312,1367,1423,1480,1538
%N A022941 a(n) = a(n-1) + c(n-2) for n >= 3, a( ) increasing, given a(1)=1, a(2)=2; where c( )
is complement of a( ).
%Y A022941 Adjacent sequences: A022938 A022939 A022940 this_sequence A022942 A022943 A022944
%Y A022941 Sequence in context: A101201 A033096 A152738 this_sequence A007982 A011904 A047809
%K A022941 nonn
%O A022941 1,2
%A A022941 Clark Kimberling (ck6(AT)evansville.edu)

(for the even-indexed terms, where c() gives the odd-indexed terms)

Still worth submitting, after correction, with definition
mentioning A022941.

Neil

```