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 A074735 #11 Jan 25 2025 16:33:34
%S A074735 0,3,1,2,0,3,2,8,0,1,1,1,0,3,3,2,0,2,1,3,0,2,2,2,0,1,1,1,0,7,4,4,0,4,
%T A074735 1,2,0,4,2,3,0,1,1,1,0,2,3,4,0,2,1,8,0,4,2,3,0,1,1,1,0,6,5,4,0,3,1,2,
%U A074735 0,5,2,4,0,1,1,1,0,5,3,2,0,2,1,3,0,2,2,2,0,1,1,1,0,4,4,5,0,6,1,2,0,3,2,5,0
%N A074735 Number of steps to reach an integer starting with (n+3)/4 and iterating the map x -> x*ceiling(x).
%C A074735 Let S(n) = Sum_{k=1..n} a(k) then it seems that S(n) is asymptotic to 2n. S(n)=2n for many values of n, namely n=10,128,198,199,237,238,241,242,246,247,249,267,329... More generally, starting with (n+2^m-1)/2^m and iterating the same map seems to produce the same kind of behavior for a(n) (i.e., Sum_{k=1..n} a(k) is asymptotic to c(m)*n where c(m) depends on m and c(m) is a power of 2).
%F A074735 Special cases: for k>= 0 a(4k+1) = 0, a(16k+10) = a(16k+11) = a(16k+12) = 1.
%t A074735 Table[Length[NestWhileList[# Ceiling[#]&,(n+3)/4,!IntegerQ[#]&]]-1,{n,110}] (* _Harvey P. Dale_, Apr 11 2020 *)
%o A074735 (PARI) a(n)=if(n<0,0,s=(n+3)/4; c=0; while(frac(s)>0,s=s*ceil(s); c++); c)
%Y A074735 Cf. A073524, A073341, A068119.
%K A074735 nonn
%O A074735 1,2
%A A074735 _Benoit Cloitre_, Sep 05 2002
%E A074735 Offset corrected by _Sean A. Irvine_, Jan 25 2025