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

0,3

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

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

Cf. A109812, A121216.

Sequence in context: A026182 A026198 A026206 * A117606 A245814 A060736

Adjacent sequences: A353705 A353706 A353707 * A353709 A353710 A353711

Keyword

nonn

Author

N. J. A. Sloane, May 06 2022

Status

approved