[seqfan] A1: In binary representation, a(n)^2 is the smallest square with n^2 as substring.

[zak seidov]

While OEIS on vacation...

%N A1 In binary representation, 
a(n)^2  is the smallest square 
with n^2 as substring.

%S 2,3,5,8,10,10,14,16,18,20,22,17,26,28,30,32,34,36,38,
40,42,44,46,40,50,52,54,56,58,60,62,64,66,68,70

%C 
In most cases a(n)=a(n-1)+2 but the sequence is not monotonic:

the terms a(n) which are less than previous ones, a(n)<a(n-1), are:
a(n)=17,40,80,99,160,320,640,577,1280,
with corresponding n: 12,24,48,70,96,192,384,408,768.

Q Are all n=12*k giving a(n)=40*k for k>2?

%e
a(12)=17 because 12^2=144=10010000_2, and 17^2=289=1010001(10010000)01_2.

See
http://zak08.livejournal.com/14344.html

Thanks, 
Zak