[seqfan] Re: Underline a(n) when n=3k

[Vladimir Shevelev]

Interesting sequence!

By the definition, we have

x_n=a(n)=a(floor((3*n-1)/2))=a(3*n).

So, if the initial values x_1=a, x_2=b, then

a=x_1=x_3=x_4=x_5=x_7=x_9=x_10=x_12=x_13=x=14=...
b=x_2=x_6=x_8=x_11=x_16=x_18=x_23=x_24=x_26=...

Thus we have (a,b)-sequence with the indices of a
A(n)=1,3,4,5,7,9,10,12,13,14,15,17,19,... and the indices of b
B(n)=2,6,8,11,16,18,23,24,26,33,34,35,38,...
It is interesting, what are liminf(A(n)/n) and limsup(A(n)/n)?
The sequence when B(n)=2*A(n) is  1,2,3,6,8,9,13,...
Many interesting new sequences and questions characterize
a good initial sequence.

Thanks, Eric!
Vladimir


________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Eric Angelini [Eric.Angelini at kntv.be]
Sent: 05 March 2015 20:27
To: Sequence Fanatics Discussion list
Subject: [seqfan] Underline a(n) when n=3k

Hello SeqFans,

S = 1,2,1,1,1,2,1,2,1,1,2,1,1,1,1,2,1,2,1,1,1,1,2,2,1,2,1,1,1,1,1,1,2,2,2,1,1,2,1,1,1,1,1,1,1,1,1,2,2,2,1,2,1,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,2,2,2,2,1,1,2,2,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,...

Underline a(n) when n=3k (k = 1-->oo).
The underlined terms reproduce S.
The non underlined terms reproduce S too.

Best,
É.





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