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A353708
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.
4
0, 1, 2, 4, 5, 3, 8, 12, 6, 16, 9, 7, 18, 24, 13, 32, 34, 10, 17, 20, 14, 11, 33, 36, 22, 19, 40, 44, 21, 64, 42, 15, 65, 48, 26, 66, 37, 25, 72, 38, 23, 73, 96, 50, 27, 68, 100, 35, 128, 28, 29, 67, 98, 52, 129, 74, 30, 49, 97, 70, 130, 41, 45, 80, 82, 39, 132, 88, 43, 131, 84, 56, 136, 69, 51, 58, 76, 133, 144, 90, 46, 160, 81, 31, 134, 192, 57, 47
OFFSET
0,3
COMMENTS
A set-theory analog of A121216.
This is a permutation of the nonnegative numbers.
MAPLE
read(transforms) : # ANDnos def'd here
A353708 := 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 then
return c;
end if;
end do:
end if;
end proc: # Following R. J. Mathar's program for A109812.
[seq(A353708(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
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 = 87; 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 - 2], k] == 0], k++]; Set[{a[n], c[k]}, {k, n}]; If[k == u, While[c[u] > -1, u++]], {n, 2, nn}]; Array[a, nn + 1, 0] (* Michael De Vlieger, May 06 2022 *)
CROSSREFS
Sequence in context: A026182 A026198 A026206 * A117606 A245814 A060736
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 06 2022
STATUS
approved