A351886 - OEIS

%I #16 Mar 01 2022 14:51:24

%S 0,1,2,1,4,2,3,1,8,4,6,3,8,3,4,1,16,9,11,6,14,5,8,4,17,9,10,5,10,3,5,

%T 1,32,16,21,10,24,12,15,7,26,11,17,7,16,6,11,4,39,19,20,10,24,10,11,4,

%U 26,12,15,7,12,3,6,1,64,34,34,20,41,21,21,10,45,21

%N a(n) is the number of k < n such that a(k) AND n = 0 (where AND denotes the bitwise AND operator).

%C The definition is recursive: a(n) depends on prior terms (a(0), ..., a(n-1)); a(0) = 0 corresponds to an empty sum.

%H Rémy Sigrist, <a href="/A351886/b351886.txt">Table of n, a(n) for n = 0..10000</a>

%F a(2^k) = 2^k.

%e The first terms, alongside the corresponding k's, are:

%e   n   a(n)  k's

%e   --  ----  -------------------------

%e    0     0  {}

%e    1     1  {0}

%e    2     2  {0, 1}

%e    3     1  {0}

%e    4     4  {0, 1, 2, 3}

%e    5     2  {0, 2}

%e    6     3  {0, 1, 3}

%e    7     1  {0}

%e    8     8  {0, 1, 2, 3, 4, 5, 6, 7}

%e    9     4  {0, 2, 4, 5}

%e   10     6  {0, 1, 3, 4, 7, 9}

%e   11     3  {0, 4, 9}

%e   12     8  {0, 1, 2, 3, 5, 6, 7, 11}

%p a:= proc(n) option remember; add(

%p      `if`(Bits[And](n, a(j))=0, 1, 0), j=0..n-1)

%p     end:

%p seq(a(n), n=0..80);  # _Alois P. Heinz_, Feb 28 2022

%o (PARI) for (n=1, #a=vector(75), print1 (a[n]=sum(k=1, n-1, bitand(a[k], n-1)==0)", "))

%o (Python)

%o a = []

%o [a.append(sum(a[k] & n == 0 for k in range(n))) for n in range(74)]

%o print(a) # _Michael S. Branicky_, Feb 24 2022

%Y Cf. A080100, A088167, A350677, A351887.

%K nonn,base

%O 0,3

%A _Rémy Sigrist_, Feb 23 2022