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

1, 2, 3, 4, 6, 9, 14, 21, 32, 48, 72, 108, 162, 243, 364, 546, 819, 1228, 1842, 2763, 4144, 6216, 9324, 13986, 20979, 31468, 47202, 70803, 106204, 159306, 238959, 358438, 537657, 806486, 1209729, 1814594, 2721891, 4082836, 6124254, 9186381, 13779572, 20669358, 31004037

Offset: 1

Author

Jason Atwood, Oct 09 2019

Keywords

• nonn

Comments

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.

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

Links

• Robert Israel, Table of n, a(n) for n = 1..5657

Crossrefs

Similar to A061418, which always rounds down.

Programs

Maple

R:= 1: r:= 1:
for i from 1 to 100 do
  r:= r*3/2;
  if not r::integer then
    v:= floor(r);
    if v::even then r:= v else r:= v+1 fi;
  fi;
  R:= R,r;
od:
R; # Robert Israel, Jan 10 2023

Mathematica

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 *)
NestList[Round[(3#)/2]&,1,50] (* Harvey P. Dale, Jul 22 2025 *)

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