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 A076092 #20 Mar 19 2025 18:31:45
%S A076092 1,0,-1,0,1,2,1,0,-1,-2,-1,-2,-3,-2,-1,0,-1,0,1,2,3,2,1,2,3,4,5,4,3,2,
%T A076092 1,0,1,2,3,2,1,0,-1,-2,-3,-4,-3,-2,-1,0,1,0,-1,-2,-3,-4,-5,-6,-7,-6,
%U A076092 -5,-4,-3,-2,-1,0,1,2,1,0,-1,-2,-3,-4,-5,-4,-5,-4,-5,-4,-3,-2,-1,0,1,2,3,4,5,4,3,2,1,0,-1,-2,-3,-4,-5,-4,-5,-4,-3
%N A076092 a(n) = n - 2*Sum_{i=1..n} A076182(i).
%C A076092 Recall the modified Collatz map: x->x/2 if x is even; x->(3x+1)/2 if x is odd. Let C_m(n) denotes the image of n after m iterations. Then b(n) = A076182(n) = (lim_{k->infinity} C_2k(n))-1 (from the Collatz conjecture C_2k(n) is constant = 1 or 2 for k sufficiently large).
%C A076092 Curiously the graph of a(n) has "regularities" around 0 and a pattern that becomes larger and larger when compared with a random sequence of the form n - 2*Sum_{k=1..n} r(k) where r(k) takes random values from (0;1).
%H A076092 Hugo Pfoertner, <a href="/A076092/b076092.txt">Table of n, a(n) for n = 1..10000</a>
%e A076092 b(12)=1 since, starting with 12, the Collatz map gives: 12->6->3->5->8->4->2->1, then C_6(12)=2 and then b(12) = C_6(12)-1 = 1.
%o A076092 (PARI) a(n)=n-2*sum(i=1,n,if(i<0,0,s=i; c=0; while(s>1,s=(s%2)*(3*s+1)/2+(1-s%2)*s/2; c++); c)%2)
%Y A076092 Cf. A076182 (b(n) sequence).
%K A076092 sign,look
%O A076092 1,6
%A A076092 _Benoit Cloitre_, Nov 01 2002
%E A076092 Revised by _Sean A. Irvine_, Mar 19 2025