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A328262 a(n) = a(n-1)*3/2, if noninteger then rounded to the nearest even integer, with a(1) = 1.

%I A328262 #33 Jul 22 2025 16:16:27
%S A328262 1,2,3,4,6,9,14,21,32,48,72,108,162,243,364,546,819,1228,1842,2763,
%T A328262 4144,6216,9324,13986,20979,31468,47202,70803,106204,159306,238959,
%U A328262 358438,537657,806486,1209729,1814594,2721891,4082836,6124254,9186381,13779572,20669358,31004037
%N A328262 a(n) = a(n-1)*3/2, if noninteger then rounded to the nearest even integer, with a(1) = 1.
%C A328262 On average, about one out of every three numbers will have been rounded, since after each rounding there is a 1 in 1 chance of the next number being divisible by 2, 1 in 2 of being divisible by 2^2, and so on, leading to an average of the number after a rounding being divisible by 2^2, requiring three terms (including itself) to reach a point where it needs to round again. There doesn't seem to be any pattern to whether the roundings are up or down, and they seem to each be equally likely.
%C A328262 Because the Mathematica function "Round" always rounds x.5 to the nearest even integer to x, the second Mathematica program below is very simple. - _Harvey P. Dale_, Jul 22 2025
%H A328262 Robert Israel, <a href="/A328262/b328262.txt">Table of n, a(n) for n = 1..5657</a>
%p A328262 R:= 1: r:= 1:
%p A328262 for i from 1 to 100 do
%p A328262   r:= r*3/2;
%p A328262   if not r::integer then
%p A328262     v:= floor(r);
%p A328262     if v::even then r:= v else r:= v+1 fi;
%p A328262   fi;
%p A328262   R:= R,r;
%p A328262 od:
%p A328262 R; # _Robert Israel_, Jan 10 2023
%t A328262 f[n_] := If[EvenQ[n], 3n/2, 1 + (3n - Mod[n, 4])/2]; a[1] = 1; a[n_] := a[n] = f[a[n - 1]]; Array[a, 36] (* _Amiram Eldar_, Oct 12 2019 *)
%t A328262 NestList[Round[(3#)/2]&,1,50] (* _Harvey P. Dale_, Jul 22 2025 *)
%o A328262 (PARI) seq(n)={my(a=vector(n)); a[1]=1; for(n=2, n, my(t=a[n-1]*3); if(t%2, t+=t%4-2); a[n]=t/2); a} \\ _Andrew Howroyd_, Oct 11 2019
%Y A328262 Similar to A061418, which always rounds down.
%K A328262 nonn
%O A328262 1,2
%A A328262 _Jason Atwood_, Oct 09 2019