This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A173022 #19 Apr 02 2025 05:16:22
%S A173022 1,1,1,2,2,2,3,4,4,4,4,4,5,5,6,7,7,7,7,7,7,7,7,7,8,8,8,9,10,10,11,12,
%T A173022 12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,14,14,14,15,
%U A173022 16,17,17,17,18,19,19,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21
%N A173022 Number of numbers <= n whose binary representation is without isolated ones.
%H A173022 Reinhard Zumkeller, <a href="/A173022/b173022.txt">Table of n, a(n) for n = 0..10000</a>
%F A173022 a(A144795(n+1)) = a(A144795(n)) + 1.
%F A173022 a(2^n - 1) = A005251(n+2).
%F A173022 A173021(n) <= a(n) <= A173023(n).
%e A173022 a(20) = #{0,3,6,7,12,14,15} = #{0,11,110,111,1100,1110,1111} = 7.
%t A173022 Accumulate[Array[Boole[FreeQ[Split[IntegerDigits[#, 2]], {1}]] &, 100, 0]] (* _Paolo Xausa_, Oct 15 2024 *)
%Y A173022 Cf. A005251, A007088, A144795, A173021, A173023.
%K A173022 base,nonn
%O A173022 0,4
%A A173022 _Reinhard Zumkeller_, Feb 07 2010