Jason Atwood - cp's OEIS frontend

User: Jason Atwood

Jason Atwood has authored 2 sequences.

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

Jason Atwood, Oct 09 2019

nonn

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

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

Similar to A061418, which always rounds down.

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

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 *)

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

A323558 Numbers k such that n^2 + n + k has no prime factor p <= 41 for any integer n.

Original entry on oeis.org

19421, 27941, 55661, 72491, 237761, 333491, 514037, 546587, 553997, 601037, 619517, 635807, 685667, 712421, 843497, 849701, 871457, 916031, 994907, 1024691, 1049297, 1084607, 1084997, 1103777, 1165181, 1196927, 1211291, 1240697, 1262201, 1292231, 1342037, 1376591, 1384907, 1438751, 1454897, 1462577, 1488647

Offset: 1

Jason Atwood, Jan 17 2019

nonn

Observation: The terms tend to be primes but are not by any means all primes.
If k is a term, then k + A002110(13) = k + 304250263527210 is also a term.
It appears this sequence includes about 1/2918.52 of the positive integers.

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User: Jason Atwood

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

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A323558 Numbers k such that n^2 + n + k has no prime factor p <= 41 for any integer n.

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