OFFSET
1,2
COMMENTS
If n appears then 2n and 3n do not. - Benoit Cloitre, Jun 13 2002
Closed under multiplication. Each term is a product of a unique subset of {6} U A050376 \ {2,3}. - Peter Munn, Sep 14 2019
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
Don McDonald, Obituary of Alan Robert Boyd, posted to sci.math Jan 02 1999; alternative link.
FORMULA
a(n) = 12/7 * n + O(log^2 n). - Charles R Greathouse IV, Sep 10 2015
{a(n)} = A052330({A014601(n)}), where {a(n)} denotes the set of integers in the sequence. - Peter Munn, Sep 14 2019
MAPLE
N:= 1000: # to get all terms up to N
A:= {seq(2^i, i=0..ilog2(N))}:
Ae, Ao:= selectremove(issqr, A):
Be:= map(t -> seq(t*9^j, j=0 .. floor(log[9](N/t))), Ae):
Bo:= map(t -> seq(t*3*9^j, j=0..floor(log[9](N/(3*t)))), Ao):
B:= Be union Bo:
C1:= map(t -> seq(t*(6*i+1), i=0..floor((N/t -1)/6)), B):
C2:= map(t -> seq(t*(6*i+5), i=0..floor((N/t - 5)/6)), B):
A036668:= C1 union C2; # Robert Israel, May 09 2014
MATHEMATICA
a = {1}; Do[AppendTo[a, NestWhile[# + 1 &, Last[a] + 1,
Apply[Or, Map[MemberQ[a, #] &, Select[Flatten[{#/3, #/2}],
IntegerQ]]] &]], {150}]; a (* A036668 *)
(* Peter J. C. Moses, Apr 23 2019 *)
PROG
(PARI) twos(n) = {local(r, m); r=0; m=n; while(m%2==0, m=m/2; r++); r}
threes(n) = {local(r, m); r=0; m=n; while(m%3==0, m=m/3; r++); r}
isA036668(n) = (twos(n)+threes(n))%2==0 \\ Michael B. Porter, Mar 16 2010
(PARI) is(n)=(valuation(n, 2)+valuation(n, 3))%2==0 \\ Charles R Greathouse IV, Sep 10 2015
(PARI) list(lim)=my(v=List(), N); for(n=0, logint(lim\=1, 3), N=if(n%2, 2*3^n, 3^n); while(N<=lim, forstep(k=N, lim, [4*N, 2*N], listput(v, k)); N<<=2)); Set(v) \\ Charles R Greathouse IV, Sep 10 2015
(Python)
from itertools import count
def A036668(n):
def f(x):
c = n+x
for i in range(x.bit_length()+1):
i2 = 1<<i
for j in count(i&1, 2):
k = i2*3**j
if k>x:
break
m = x//k
c -= (m-1)//6+(m-5)//6+2
return c
m, k = n, f(n)
while m != k: m, k = k, f(k)
return m # Chai Wah Wu, Jan 28 2025
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
N. J. A. Sloane, Antreas P. Hatzipolakis (xpolakis(AT)hol.gr)
EXTENSIONS
Offset changed by Chai Wah Wu, Jan 28 2025
STATUS
approved