cp's OEIS Frontend

A087118 Numbers having exactly one maximal group of consecutive zeros in binary representation of n.

%I A087118 #36 Apr 12 2019 08:27:18
%S A087118 0,2,4,5,6,8,9,11,12,13,14,16,17,19,23,24,25,27,28,29,30,32,33,35,39,
%T A087118 47,48,49,51,55,56,57,59,60,61,62,64,65,67,71,79,95,96,97,99,103,111,
%U A087118 112,113,115,119,120,121,123,124,125,126,128,129,131,135,143,159,191
%N A087118 Numbers having exactly one maximal group of consecutive zeros in binary representation of n.
%C A087118 A087116(a(n)) = 1.
%C A087118 a(n) = A043687(n-1) for 1 < n < 1000. - _Georg Fischer_, Oct 19 2018
%H A087118 Gheorghe Coserea, <a href="/A087118/b087118.txt">Table of n, a(n) for n = 1..12343</a>
%H A087118 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A087118 From _Gheorghe Coserea_, Sep 28-30 2015: (Start)
%F A087118 a((n^3 - n)/6 + 2) = 2^n for n >= 1.
%F A087118 a((n^3 - n)/6 + 2 + n) = 2^n + 2^(n-1) for n >= 2.
%F A087118 a((n^3 - n)/6 + 2 + n + n-1) = 2^n + 2^(n-1) + 2^(n-2) for n >= 3.
%F A087118 a(n) < 2*2^((6*n)^(1/3)) and limsup a(n)/2^((6*n)^(1/3)) = 2.
%F A087118 a(n) > 1/2 * 2^((6*n)^(1/3)) for n>=3 and 1/2 <= liminf a(n)/(2^((6*n)^(1/3))) <= 1.
%F A087118 (End)
%p A087118 0, seq(seq(seq(2^n - 2^b + 2^a - 1, a=0..b-1),b=n-1..1,-1),n=0..10); # _Robert Israel_, Oct 01 2015
%t A087118 Table[2^n - 2^b + 2^a - 1, {n, 0, 10}, {b, n-1, 1, -1}, {a, 0, b-1}] // Flatten // Prepend[#, 0]& (* _Jean-François Alcover_, Apr 11 2019, after  _Robert Israel_ *)
%o A087118 (PARI)
%o A087118 num(a,b,c) = (1 << (a+b+c)) - (1 << (b+c)) + (1 << c)  - 1;
%o A087118 succ(a,b,c) = {
%o A087118     if (b > 1, return([a, b-1, c+1]));
%o A087118     if (c > 0, return([a+1, c, 0]));
%o A087118     return([1, a+1, 0]);
%o A087118 };
%o A087118 seq(n) = {
%o A087118     my(a = 1, b = 1, c = 0, v = vector(n));
%o A087118     for (i = 2, n, v[i] = num(a,b,c);
%o A087118          my(x = succ(a,b,c)); a = x[1]; b = x[2]; c = x[3]);
%o A087118     return(v);
%o A087118 };
%o A087118 seq(64)  \\ _Gheorghe Coserea_, Sep 28 2015
%Y A087118 Cf. A007088, A023416, A043687, A087119.
%K A087118 nonn
%O A087118 1,2
%A A087118 _Reinhard Zumkeller_, Aug 14 2003