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

1,2

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.

Links

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

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 *)

Prog

(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

Crossrefs

Similar to A061418, which always rounds down.

Sequence in context: A005428 A355910 A143951 * A292800 A214041 A058355

Adjacent sequences: A328259 A328260 A328261 * A328263 A328264 A328265

Keyword

nonn

Author

Jason Atwood, Oct 09 2019

Status

approved