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 A125758 #29 Aug 23 2022 10:07:33
%S A125758 4,7,13,16,22,25,31,34,40,43,49,52,58,61,67,70,76,79,85,88,94,97,103,
%T A125758 106,112,115,121,124,130,133,139,142,148,151,157,160,166,169,175,178,
%U A125758 184,187,193,196,202,205,211,214,220,223,229,232,238,241,247,250,256,259,265,268
%N A125758 Numbers congruent to 4 or 7 (mod 9).
%C A125758 For a given integer m, write its binary representation in reverse order, as in A125626, A125754, etc.; let a 0 mean "halving" and a 1 mean "k -> 3k+1". Then m specifies an operation on real numbers given by k -> f_m(k). Suppose the equation f_m(k) = k has a positive integer solution for some m. Then we conjecture that the values of k are precisely the terms of this sequence.
%C A125758 25 is a term because we have 25 -> 76 -> 38 -> 19 -> 58 -> 29 -> 88 -> 44 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 25.
%C A125758 In other words, we conjecture that this sequence coincides with A125757 sorted and with duplicates removed.
%H A125758 David Lovler, <a href="/A125758/b125758.txt">Table of n, a(n) for n = 1..1000</a>
%H A125758 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A125758 From _R. J. Mathar_, Apr 03 2009: (Start)
%F A125758 a(n) = a(n-1) + a(n-2) - a(n-3) = a(n-2) + 9.
%F A125758 a(n) + a(n+1) = A017185(n).
%F A125758 G.f.: x*(4+3*x+2*x^2)/((1+x)*(x-1)^2). (End)
%F A125758 E.g.f.: 2 + ((9*x - 5/2)*exp(x) - (3/2)*exp(-x))/2. - _David Lovler_, Aug 21 2022
%t A125758 Select[Range[300],MemberQ[{4,7},Mod[#,9]]&] (* _Harvey P. Dale_, Mar 12 2011 *)
%Y A125758 Cf. A125626, A125754, A125755, A125756, A125757, A125710, A125711.
%K A125758 nonn,easy
%O A125758 1,1
%A A125758 _N. J. A. Sloane_ and _David Applegate_, Feb 02 2007