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 A076087 #8 Mar 19 2025 23:33:58
%S A076087 4,5,6,1,-4,-9,-8,-4,-3,1,-4,0,4,-1,-6,-5,-1,-6,-11,-10,-9,-5,-1,0,-5,
%T A076087 -4,0,4,8,12,13,8,3,4,5,9,13,17,18,13,14,9,4,5,6,7,2,-3,1,5,9,4,-1,0,
%U A076087 1,2,-3,-2,-7,-6,-5,-10,-15,-11,-7,-3,1,-4,-9,-14,-10,-9,-8,-7,-12,-11,-10,-15,-20,-16,-15,-20,-25,-21,-17,-13,-9
%N A076087 a(n) = 7*n - 3 * Sum_{i=1..n} A006460(i).
%C A076087 Recalling the Collatz map (cf. A006370 ): x->x/2 if x is even; x->3x+1 if x is odd, let C_m(n) denotes the image of n after m iterations. Then b(n) = A006460(n) = lim_{k -> infinity} C_3k(n) (from the Collatz conjecture C_3k(n) is constant = 1, 2 or 4 for k large enough). Curiously the graph for a(n) presents "regularities" around zero and a pattern coming bigger and bigger. Compared with a random sequence of form : 7*n-3*Sum_{k=1..n} r(k) where r(k) takes random values among (1;2;4).
%e A076087 since 3->10->5->16->8->4->2->1 etc. C_6(3)=2 and then for any k>=2 C_3k(3)=2, hence b(3)=2.
%Y A076087 Cf. A006370, A006460.
%K A076087 sign
%O A076087 1,1
%A A076087 _Benoit Cloitre_, Oct 30 2002
%E A076087 Revised by _Sean A. Irvine_, Mar 19 2025