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 A099972 #19 Aug 02 2025 18:14:22
%S A099972 1,5,13,45,173,8365,73901,204973,467117,991405,5185709,13574317,
%T A099972 80683181,214900909,1288642733,3436126381,7731093677,16321028269,
%U A099972 33500897453,67860635821,136580112557,686335926445,1785847554221
%N A099972 Write 1/sqrt(2) as a binary fraction; read this from left to right and whenever a 1 appears, note the integer formed by reading leftwards from that 1.
%H A099972 Harvey P. Dale, <a href="/A099972/b099972.txt">Table of n, a(n) for n = 0..1000</a>
%e A099972 1/sqrt(2) = 0.7071067811865475244008443621048490392848359376885... = 0.10110101000001001111001100110011111110011101111001100100100001000101100101111101100010011011 in binary.
%t A099972 d = 100; l = First[RealDigits[N[1/Sqrt[2], d], 2]]; Do[m = Take[l, n]; k = Length[m]; If[m[[k]] == 1, Print[FromDigits[Reverse[m], 2]]], {n, 1, d}] (* _Ryan Propper_, Aug 18 2005 *)
%t A099972 Module[{rd=RealDigits[1/Sqrt[2],2,50][[1]],pos},pos=Flatten[Position[rd,1]];Table[ FromDigits[ Reverse[Take[rd,n]],2],{n,pos}]] (* _Harvey P. Dale_, Jul 29 2013 *)
%Y A099972 Cf. A010503, A099969, A099970, A099971, A099973, A099974.
%K A099972 nonn,easy
%O A099972 0,2
%A A099972 _N. J. A. Sloane_, Nov 13 2004, based on correspondence from _Artur Jasinski_, Mar 25 2003
%E A099972 More terms from _Ryan Propper_, Aug 18 2005