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 A323831 #20 Nov 14 2023 10:02:14 %S A323831 5,10,20,40,80,160,320,640,1280,2560,5120,10240,20480,40960,81920, %T A323831 163840,327680,6360,12720,250,5,10,20,40,80,160,320,640,1280,2560, %U A323831 5120,10240,20480,40960,81920,163840,327680,6360,12720,250 %N A323831 a(0) = 5; thereafter a(n) is obtained by doubling a(n-1) and repeatedly deleting any string of identical digits. %C A323831 Periodic with period length 20. %C A323831 Conjecture: If we start with any nonnegative number, and repeatedly double it and apply the "repeatedly delete any run of identical digits" operation described here, we eventually reach one of 0, 1, or 5. %C A323831 In other words, the conjecture is that eventually we reach 0 or join the trajectory shown here or the trajectory shown in A323830. %C A323831 The number of steps to reach 0, 1, or 5 is given in A323832. %H A323831 Paolo Xausa, <a href="/A323831/b323831.txt">Table of n, a(n) for n = 0..1000</a> %H A323831 <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1). %F A323831 a(n+1) = A321801(2*a(n)). For general numbers, the "repeatedly delete any run of identical digits" operation corresponds to repeatedly applying A321801. - _Chai Wah Wu_, Feb 11 2019 %t A323831 dad[n_]:=FromDigits[FixedPoint[Flatten[Select[Split[#],Length[#]==1&]]&,IntegerDigits[2n]]];NestList[dad,5,100] (* _Paolo Xausa_, Nov 14 2023 *) %Y A323831 Cf. A000079, A320487, A321801, A321802, A323830, A323832. %K A323831 nonn,base,easy %O A323831 0,1 %A A323831 _N. J. A. Sloane_, Feb 03 2019