[seqfan] Re: Last two digits added --> new integer rhymes
Eric Angelini
Eric.Angelini at kntv.be
Sat Feb 15 00:20:34 CET 2014
> it is not a permutation of the Naturals. For instance, 100 (or any number ending in "100") does not appear in this sequence since the last two digits of S will never sum to 0, 00, or 100
... Jim Nastos is right, sorry...
Shame on me...
My first attempt to produce a permutation
failed too; I had tried the sequence
where the word "ending", hereunder,
was replaced by "beginning".
Didn't check enough, though, the
"new" definition...
> Le 14 févr. 2014 à 20:23, "Eric Angelini" <Eric.Angelini at kntv.be> a écrit :
>
>
> Hello SeqFans,
> here is another nice permutation of the Naturals;
>
> S=1,2,3,5,8,13,4,7,11,12,23,15,6,111,
> 22,14,25,17,18,9,117,28,10,21,33,16,
> 27,19,110,31,...
>
> a(1)=1
> a(2)=2
> a(n) is the smallest integer not yet in S
> ending with the sum of the last two digits
> of S.
>
> We see after 13 that S was extended with 4
> as 1+3=4 and 4 was not yet in S;
>
> We see after 4 that S was extended with 7
> as 3+4=7 and 7 was not yet in S;
>
> We see after 7 that S was extended with 11
> as 4+7=11 and 11 was not yet in S;
>
> We see after 11 that S was extended with 12
> as 1+1=2 and 2 being already in S was replaced by 12, smallest integer
> not yet in S and ending with "2";
>
> We see after 12 that S was extended with 23
> as 1+2=3 and 3 being already in S, as 13, we used the smallest integer
> not yet in S and ending with "3";
> ...
> Best,
> É.
>
>
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