OFFSET
0,3
COMMENTS
A set-theory analog of A084937.
Conjecture: This is a permutation of the nonnegative numbers.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..16384
Walter Trump, Table of n, a(n) for n = 0..10^6
Walter Trump, Log-log plot of first 2^24 terms
MAPLE
read(transforms) : # ANDnos def'd here
A353709 := proc(n)
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.
[seq(A353709(n), n=0..256)] ;
# 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:
seq(a(n), n=0..100); # Alois P. Heinz, May 06 2022
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
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, May 06 2022
STATUS
approved