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

1,2

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A088740 A088738 A114595 * A349093 A143545 A338155

Adjacent sequences: A256412 A256413 A256414 * A256416 A256417 A256418

Keyword

nonn

Author

N. J. A. Sloane, Apr 05 2015

Status

approved