A256415 Positive integers with primes p replaced by 2p and also 3p replaced by 2p.

1, 4, 6, 4, 10, 4, 14, 8, 6, 10, 22, 12, 26, 14, 10, 16, 34, 18, 38, 20, 14, 22, 46, 24, 25, 26, 27, 28, 58, 30, 62, 32, 22, 34, 35, 36, 74, 38, 26, 40, 82, 42, 86, 44, 45, 46, 94, 48, 49, 50, 34, 52, 106, 54, 55, 56, 38, 58, 118, 60, 122, 62, 63, 64, 65, 66, 134, 68, 46, 70

Offset: 1

Author

N. J. A. Sloane, Apr 05 2015

Keywords

• nonn

Comments

The smoothed version of A064413 (A256417) is a rearrangement of these terms.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A010051, A064413, A256416 (the sorted sequence), A256417.

Programs

Haskell

a256415 n | a010051 n == 1 = 2 * n
          | r == 0 && a010051 n' == 1 = 2 * n'
          | otherwise = n
          where (n', r) = divMod n 3
-- Reinhard Zumkeller, Apr 05 2015

Maple

# Apply p->2p, 3p->2p to a sequence t1
SMOOTH:=proc(t1) local M,t2,n; t2:=[]: M:=nops(t1):
for n from 1 to M do
if isprime(t1[n]) then t2:=[op(t2),2*t1[n]];
elif (t1[n] mod 3 = 0 ) and isprime(t1[n]/3) then t2:=[op(t2),2*t1[n]/3];
else t2:=[op(t2),t1[n]]; fi; od: t2; end;
SMOOTH([seq(n,n=1..200)]);

Mathematica

Range[70] /. {n_ /; PrimeQ[n] -> 2n, n_ /; PrimeQ[n/3] -> 2n/3} (* Jean-François Alcover, Aug 04 2018 *)
Table[Which[PrimeQ[n],2n,PrimeQ[n/3],2 n/3,True,n],{n,120}] (* Harvey P. Dale, Jun 08 2019 *)