

A328262


a(n) = a(n1)*3/2, if noninteger then rounded to the nearest even integer, with a(1) = 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
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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



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:


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[n1]*3); if(t%2, t+=t%42); a[n]=t/2); a} \\ Andrew Howroyd, Oct 11 2019


CROSSREFS

Similar to A061418, which always rounds down.


KEYWORD

nonn


AUTHOR



STATUS

approved



