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.

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

Author

N. J. A. Sloane, May 06 2022

Keywords

• nonn

Comments

A set-theory analog of A121216.

This is a permutation of the nonnegative numbers.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..16384 (a(n) for n = 0..748 by N. J. A. Sloane)
• Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

Cf. A109812, A121216.

Programs

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 *)