cp's OEIS Frontend

A272681 Smallest binary square that begins with the binary expansion of n.

%I A272681 #19 May 23 2016 08:06:41
%S A272681 0,1,100,11001,100,1010001,11001,1111001,10000,1001,1010001,101101001,
%T A272681 11001,110111001,11100001,1111001,10000,10001000001,100100,1001110001,
%U A272681 1010001,10101001,101101001,10111110001,110001,11001,1101001001,110111001,11100001,111010001001
%N A272681 Smallest binary square that begins with the binary expansion of n.
%D A272681 Allan C. Wechsler, posting to math-fun mailing list May 22 2016.
%H A272681 Chai Wah Wu, <a href="/A272681/b272681.txt">Table of n, a(n) for n = 0..10000</a>
%e A272681 a(10)=1010001 = 81_10, because 1010001_2 begins with 1010 = 10_2.
%o A272681 (Python)
%o A272681 from gmpy2 import isqrt
%o A272681 def A272681(n):
%o A272681     if n == 0:
%o A272681         return 0
%o A272681     else:
%o A272681         d, nd = 1, n
%o A272681         while True:
%o A272681             x = (isqrt(nd-1)+1)**2
%o A272681             if x < nd+d:
%o A272681                 return int(bin(x)[2:])
%o A272681             d *= 2
%o A272681             nd *= 2 # _Chai Wah Wu_, May 22 2016
%Y A272681 Cf. A007088, A018851, A018796, A272679, A272680.
%K A272681 nonn,base,easy
%O A272681 0,3
%A A272681 _N. J. A. Sloane_, May 22 2016
%E A272681 More terms from _Chai Wah Wu_, May 22 2016