[seqfan] Last two digits added --> new integer rhymes
Eric Angelini
Eric.Angelini at kntv.be
Fri Feb 14 20:23:16 CET 2014
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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