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%I #12 Jan 10 2024 16:32:32
%S 0,0,2,0,7,0,0,0,15,6,10,0,3,0,0,0,31,14,30,12,23,4,16,0,7,6,2,0,3,0,
%T 0,0,63,30,62,28,63,28,56,24,47,14,42,8,35,0,32,0,15,14,14,12,7,4,0,0,
%U 7,6,2,0,3,0,0,0,127,62,126,60,127,60,120,56,127,62
%N For any number n with binary expansion (b(1), b(2), ..., b(k)), the binary expansion of a(n) is (1-floor((b(k)+b(1)+b(2))/2), 1-floor((b(1)+b(2)+b(3))/2), ..., 1-floor((b(k-1)+b(k)+b(1))/2)).
%C This sequence is a variant of A342698; here the value of the k-th bit of a(n) is the less frequent value in the bit triple centered around the k-th bit of n.
%H Rémy Sigrist, <a href="/A342700/b342700.txt">Table of n, a(n) for n = 0..8191</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(n) + A342698(n) = A003817(n).
%F a(n) = n iff n belongs to A020988.
%e The first terms, in decimal and in binary, are:
%e n a(n) bin(n) bin(a(n))
%e -- ---- ------ ---------
%e 0 0 0 0
%e 1 0 1 0
%e 2 2 10 10
%e 3 0 11 0
%e 4 7 100 111
%e 5 0 101 0
%e 6 0 110 0
%e 7 0 111 0
%e 8 15 1000 1111
%e 9 6 1001 110
%e 10 10 1010 1010
%e 11 0 1011 0
%e 12 3 1100 11
%e 13 0 1101 0
%e 14 0 1110 0
%e 15 0 1111 0
%o (PARI) a(n) = my (w=#binary(n)); sum(k=0, w-1, ((bittest(n, (k-1)%w)+bittest(n, k%w)+bittest(n, (k+1)%w))<=1) * 2^k)
%Y Cf. A003817, A020988 (fixed points), A342698.
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Mar 18 2021
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