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%I #17 Mar 27 2021 11:26:02
%S 0,0,0,1,0,1,3,3,0,0,2,3,6,7,7,7,0,0,0,1,4,5,7,7,12,12,14,15,14,15,15,
%T 15,0,0,0,1,0,1,3,3,8,8,10,11,14,15,15,15,24,24,24,25,28,29,31,31,28,
%U 28,30,31,30,31,31,31,0,0,0,1,0,1,3,3,0,0,2,3,6
%N For any number n with binary expansion Sum_{k >= 0} b(k) * 2^k, the binary expansion of a(n) is Sum_{k >= 0} floor((b(k) + b(k+1) + b(k+2))/2) * 2^k.
%C The value of the k-th bit in a(n) corresponds to the most frequent value in the bit triple starting at the k-th bit in n.
%H Rémy Sigrist, <a href="/A342697/b342697.txt">Table of n, a(n) for n = 0..8192</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F a(n) = 0 iff n belongs to A048715.
%F a(n) = floor(A048730(n)/8) = floor(A048733(n)/2). - _Kevin Ryde_, Mar 26 2021
%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 0 10 0
%e 3 1 11 1
%e 4 0 100 0
%e 5 1 101 1
%e 6 3 110 11
%e 7 3 111 11
%e 8 0 1000 0
%e 9 0 1001 0
%e 10 2 1010 10
%e 11 3 1011 11
%e 12 6 1100 110
%e 13 7 1101 111
%e 14 7 1110 111
%e 15 7 1111 111
%o (PARI) a(n) = sum(k=0, #binary(n), ((bittest(n, k)+bittest(n, k+1)+bittest(n, k+2))>=2) * 2^k)
%Y Cf. A048715, A048730, A048733, A342698, A342700.
%K nonn,base,easy
%O 0,7
%A _Rémy Sigrist_, Mar 18 2021
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