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A272679 a(n)^2 is the smallest square whose binary expansion begins with the binary expansion of n.

%I A272679 #19 May 23 2016 08:04:55
%S A272679 0,1,2,5,2,9,5,11,4,3,9,19,5,21,15,11,4,33,6,25,9,13,19,39,7,5,29,21,
%T A272679 15,61,11,45,8,23,33,67,6,49,35,25,9,73,13,53,107,19,77,39,79,7,10,81,
%U A272679 29,83,59,21,15,43,61,87,11,89,63,45,8,129,23,93,33,47
%N A272679 a(n)^2 is the smallest square whose binary expansion begins with the binary expansion of n.
%D A272679 Allan C. Wechsler, posting to math-fun mailing list May 22 2016.
%H A272679 Chai Wah Wu, <a href="/A272679/b272679.txt">Table of n, a(n) for n = 0..10000</a>
%e A272679 a(10)=9, because 9^2 = 81 = 1010001_2 begins with 1010 = 10_2.
%o A272679 (Python)
%o A272679 from gmpy2 import isqrt
%o A272679 def A272679(n):
%o A272679     if n == 0:
%o A272679         return 0
%o A272679     else:
%o A272679         d, nd = 1, n
%o A272679         while True:
%o A272679             x = isqrt(nd-1)+1
%o A272679             if x**2 < nd+d:
%o A272679                 return int(x)
%o A272679             d *= 2
%o A272679             nd *= 2 # _Chai Wah Wu_, May 22 2016
%Y A272679 Cf. A007088, A018851, A018796, A272680, A272681.
%K A272679 nonn,base,easy
%O A272679 0,3
%A A272679 _N. J. A. Sloane_, May 22 2016
%E A272679 More terms from _Chai Wah Wu_, May 22 2016