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A362757 The number of integers in the set f^n({0}), where f is a variant of the Collatz function that replaces any element x in the argument set with both x/2 and 3*x+1.

%I A362757 #43 May 10 2023 10:41:38
%S A362757 1,2,3,5,7,10,15,22,33,48,72,103,153,221,326,477,705,1036,1526,2243,
%T A362757 3310,4872,7179,10582,15620,23039,33995,50151,73999,109170,161092,
%U A362757 237629,350590,517254,763167,1126070,1661607,2451715,3617809,5338044,7876246,11621318,17147409,25300982,37331656,55082911,81275003
%N A362757 The number of integers in the set f^n({0}), where f is a variant of the Collatz function that replaces any element x in the argument set with both x/2 and 3*x+1.
%C A362757 a(n) is the number of integers in set A(n), where A(0) = {0} and A(n+1) = {x/2 : x in A(n)} union {3x+1 : x in A(n)}.
%C A362757 Non-integer numbers do not have integer offsprings. Consequently, they can be dropped when calculating terms of the sequence.
%C A362757 Apparently the limit of a(n)/a(n-1) is approximately equal to 1.47551 (see plot of a(n-1)/a(n) ~= 0.677732). An explanation of this limit would be desirable. - _Hugo Pfoertner_, May 06 2023
%H A362757 Markus Sigg, <a href="/A362757/b362757.txt">Table of n, a(n) for n = 0..70</a>
%H A362757 Hugo Pfoertner, <a href="https://oeis.org/plot2a?name1=A362757&amp;name2=A362757&amp;tform1=untransformed&amp;tform2=untransformed&amp;shift=-1&amp;radiop1=ratio&amp;drawpoints=true">Plot of ratio a(n-1)/a(n)</a>, using Plot 2.
%e A362757 a(3) = 5 is the number of integers in the set {0, 1/4, 1/2, 1, 2, 5/2, 4, 13}.
%o A362757 (PARI)
%o A362757 a362757(maxn) = {
%o A362757   my(A = Set([0]));
%o A362757   print1(1);
%o A362757   for(n = 1, maxn,
%o A362757     A = setunion([t >> 1 | t <- A, bitnegimply(1,t)], [3*t+1 | t <- A]);
%o A362757     print1(",", #A);
%o A362757   );
%o A362757 };
%Y A362757 Cf. A208127, A275544.
%K A362757 nonn
%O A362757 0,2
%A A362757 _Markus Sigg_, May 02 2023