A375776 Bitwise conflict-free sequence: Each number n is placed into the first set k that contains no element x where n AND x > 0: a(n) = k.

1, 1, 2, 1, 3, 4, 5, 1, 4, 3, 6, 2, 7, 8, 9, 1, 8, 7, 10, 6, 11, 12, 13, 5, 14, 15, 16, 17, 18, 19, 20, 1, 12, 11, 17, 10, 15, 14, 21, 13, 22, 23, 24, 25, 26, 27, 28, 2, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 1, 19, 18, 25, 16, 23, 22, 36, 10, 30, 29, 32

Offset: 1

Author

Matt Donahoe, Aug 27 2024

Keywords

• nonn
• look
• base

Examples

			For n = 1, a(1) = 1 because 1 gets put into the first set.
For n = 2, a(2) = 1 because 2 AND 1 == 0, so 2 can also be put into the first set.
For n = 3, a(3) = 2 because 3 AND 1 == 1, so 3 must be put into a new set.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..16384
• Wikipedia, Bitwise operation

Crossrefs

Cf. A000079, A164346, A279125.

Programs

Maple

s:= proc() {} end:
a:= proc(n) option remember; local k; for k
      while ormap(x-> Bits[And](x, n)>0, s(k)) do od;
      s(k):= {s(k)[], n}; k
    end:
seq(a(n), n=1..75);  # Alois P. Heinz, Aug 27 2024

PARI

seq(n)={my(a=vector(n), L=vector(n)); for(n=1, n, for(j=1, oo, if(!bitand(n,L[j]), L[j]=bitor(L[j],n); a[n]=j; break))); a} \\ Andrew Howroyd, Aug 27 2024

Python

def seq(n):
    L = [0] + [0] * n
    for i in range(1, n + 1):
        k = next((k for k in range(1, len(L)) if i & L[k] == 0), None)
        L[k] |= i
        yield k

Formula

a(n) = 1 <=> n in { A000079 }. - Andrew Howroyd, Aug 27 2024

a(n) = 2 <=> n in { A164346 }. - Alois P. Heinz, Aug 27 2024

a(n) = A279125(n) + 1. - Rémy Sigrist, Aug 30 2024