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 A195609 #17 Dec 10 2019 04:15:24
%S A195609 3,4,5,9,15,16,17,23,27,28,29,33,39,43,44,45,51,52,53,57,63,64,65,71,
%T A195609 75,76,77,83,84,85,89,95,99,100,101,105,111,112,113,119,123,124,125,
%U A195609 129,135,139,140,141,147,148,149,153,159,163,164,165,169,175,176
%N A195609 Numbers n such that Sum_{i=1..n} A(i) = A(n)*A(n+1)/4, where A(n) = A000069(n).
%C A195609 Conjectures: 1) there are only 3 different first differences 1,4,6; 2) the sequence contains either isolated series of terms, e.g., {9},{23},{33},{39},..., or series of 3 consecutive integers, e.g., {3,4,5}, {15,16,17}, etc.; 3)the first terms m of every series satisfy the condition A(m+1)-A(m-1)=5, where A(n)=A000069(n).
%H A195609 Amiram Eldar, <a href="/A195609/b195609.txt">Table of n, a(n) for n = 1..10000</a>
%t A195609 a = Select[Range[1000], OddQ[DigitCount[#, 2][[1]]] &]; t = {}; s = 0; Do[s = s + a[[n]]; If[s == a[[n]] a[[n + 1]]/4, AppendTo[t, n]], {n, Length[a] - 1}]; t (* _T. D. Noe_, Sep 23 2011 *)
%Y A195609 Cf. A000069, A174531, A001969, A195608.
%K A195609 nonn
%O A195609 1,1
%A A195609 _Vladimir Shevelev_, Sep 21 2011