

A256415


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


4



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
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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} (* JeanFrançois 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 * A143545 A328045 A277278
Adjacent sequences: A256412 A256413 A256414 * A256416 A256417 A256418


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 05 2015


STATUS

approved



