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A350677 a(n) is the sum of the numbers k < n such that a(k) AND n = 0 (where AND denotes the bitwise AND operator).

%I A350677 #28 Mar 01 2022 14:51:17
%S A350677 0,0,1,1,6,1,11,1,22,13,18,1,39,11,29,1,88,5,70,1,82,1,84,1,158,23,
%T A350677 124,1,134,1,163,1,428,151,272,73,328,117,315,87,452,185,307,97,258,
%U A350677 109,228,35,444,171,331,77,378,81,265,37,345,135,251,41,238,45,194
%N A350677 a(n) is the sum of the numbers k < n such that a(k) AND n = 0 (where AND denotes the bitwise AND operator).
%C A350677 The definition is recursive: a(n) depends on prior terms (a(0), ..., a(n-1)); a(0) = a(1) = 0 correspond to empty sums.
%H A350677 Rémy Sigrist, <a href="/A350677/b350677.txt">Table of n, a(n) for n = 0..10000</a>
%e A350677 The first terms, alongside the corresponding k's, are:
%e A350677   n   a(n)  k's
%e A350677   --  ----  --------------------------
%e A350677    0     0  {}
%e A350677    1     0  {0}
%e A350677    2     1  {0, 1}
%e A350677    3     1  {0, 1}
%e A350677    4     6  {0, 1, 2, 3}
%e A350677    5     1  {0, 1}
%e A350677    6    11  {0, 1, 2, 3, 5}
%e A350677    7     1  {0, 1}
%e A350677    8    22  {0, 1, 2, 3, 4, 5, 7}
%e A350677    9    13  {0, 1, 4, 8}
%e A350677   10    18  {0, 1, 2, 3, 5, 7}
%e A350677   11     1  {0, 1}
%e A350677   12    39  {0, 1, 2, 3, 5, 7, 10, 11}
%p A350677 a:= proc(n) option remember; add(
%p A350677      `if`(Bits[And](n, a(j))=0, j, 0), j=0..n-1)
%p A350677     end:
%p A350677 seq(a(n), n=0..80);  # _Alois P. Heinz_, Feb 28 2022
%o A350677 (PARI) for (n=1, #a=vector(63), print1 (a[n]=sum(k=1, n-1, if (bitand(a[k], n-1)==0, k-1, 0))", "))
%Y A350677 Cf. A350802, A351886.
%K A350677 base,nonn
%O A350677 0,5
%A A350677 _Rémy Sigrist_, Feb 25 2022