|
|
A353709
|
|
a(0)=0, a(1)=1; thereafter a(n) = smallest nonnegative integer not among the earlier terms of the sequence such that a(n) and a(n-2) have no common 1-bits in their binary representations and also a(n) and a(n-1) have no common 1-bits in their binary representations.
|
|
21
|
|
|
0, 1, 2, 4, 8, 3, 16, 12, 32, 17, 6, 40, 64, 5, 10, 48, 65, 14, 128, 33, 18, 68, 9, 34, 20, 72, 35, 132, 24, 66, 36, 25, 130, 96, 13, 144, 98, 256, 21, 42, 192, 257, 22, 104, 129, 258, 28, 97, 384, 26, 37, 320, 136, 7, 80, 160, 11, 84, 288, 131, 76, 272, 161, 70, 264, 49, 134, 328, 512, 19, 44, 448, 513, 30, 224, 768, 15, 112, 640, 259, 52, 200, 514, 53
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Conjecture: This is a permutation of the nonnegative numbers.
|
|
LINKS
|
|
|
MAPLE
|
read(transforms) : # ANDnos def'd here
option remember;
local c, i, known ;
if n <= 2 then
n;
else
for c from 1 do
known := false ;
for i from 1 to n-1 do
if procname(i) = c then
known := true;
break ;
end if;
end do:
if not known and ANDnos(c, procname(n-2)) = 0 and ANDnos(c, procname(n-1)) = 0 then
return c;
end if;
end do:
end if;
end proc: # Following R. J. Mathar's program for A109812.
# second Maple program:
b:= proc() false end: t:= 2:
a:= proc(n) option remember; global t; local k; if n<2 then n
else for k from t while b(k) or Bits[And](k, a(n-2))>0
or Bits[And](k, a(n-1))>0 do od; b(k):=true;
while b(t) do t:=t+1 od; k fi
end:
|
|
MATHEMATICA
|
nn = 83; c[_] = -1; a[0] = c[0] = 0; a[1] = c[1] = 1; u = 2; Do[k = u; While[Nand[c[k] == -1, BitAnd[a[n - 1], k] == 0, BitAnd[a[n - 2], k] == 0], k++]; Set[{a[n], c[k]}, {k, n}]; If[k == u, While[c[u] > -1, u++]], {n, 2, nn}], n]; Array[a, nn+1, 0] (* Michael De Vlieger, May 06 2022 *)
|
|
PROG
|
(Python)
from itertools import count, islice
def A353709_gen(): # generator of terms
s, a, b, c, ab = {0, 1}, 0, 1, 2, 1
yield from (0, 1)
while True:
for n in count(c):
if not (n & ab or n in s):
yield n
a, b = b, n
ab = a|b
s.add(n)
while c in s:
c += 1
break
|
|
CROSSREFS
|
Cf. A084937 (number theory analog), A109812, A121216, A353405 (powers of 2), A353708, A353710, A353715 and A353716 (a(n)+a(n+1)), A353717 (inverse), A353718, A353719 (primes), A353720 and A353721 (Records).
For the numbers that are the slowest to appear see A353723 and A353722.
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|