Splitting of sequences

[Lallouet]

I built the following sequence :

1(n) :1,1,2,3,2,4,5,3,6,7,4,8,5,10,11,6,12,13,7,14,15,,8,16,17

If  we delete the term 1(1(1))+1 , i.e the second term, it remains 2(n) : 1,2,3,4,5,3,6,7,4,8,9,5,10,11

 From this we delete b(b(2)+2) i;e the 2+2=4th term and we reitere the process by deleting at the stage k the term k(k(k))+k)

At the limit it remains the set of natural numbers N in growing order.

Moreover the sequence built with the successive deleted terms is  also N.

If this sequence may appear original at the first look, i'ts not true at all. Indeed,starting from any pair of sequences, it's easy to blend them in an unic one which may be 

split into  the two originals sequences by the same procedure.

For example, for fun, I built the following sequence :3,1,7,2,4,1,8,5,1,9,2,6,1,2,5,3,5,8,8,8,8,2,9,7,9,4,3,2,3,5,..... whose splitting gives the digits of pi and of e.

Taking in account the lack of originality, i don't think that any of these sequences worths to be published in EOIS except if Neil wishes to publish one of this type as 

example, which has maybe already been made what i was enable to verify. The problem will be then to choose  the most pleasant foundress sequences.

I hope not to have disturb you too much with such a light subject.

Best regards to all all of you. Have a happy 1st of may

Philippe LALLOUET
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