|
%I #12 Jan 10 2024 16:31:22
%S 0,1,1,3,0,7,7,7,0,9,5,15,12,15,15,15,0,17,1,19,8,27,15,31,24,25,29,
%T 31,28,31,31,31,0,33,1,35,0,35,7,39,16,49,21,55,28,63,31,63,48,49,49,
%U 51,56,59,63,63,56,57,61,63,60,63,63,63,0,65,1,67,0,67,7
%N For any number n with binary expansion (b(1), b(2), ..., b(k)), the binary expansion of a(n) is (floor((b(k)+b(1)+b(2))/2), floor((b(1)+b(2)+b(3))/2), ..., floor((b(k-1)+b(k)+b(1))/2)).
%C This sequence is a variant of A342697; here we deal with bit triples in a "cyclic" binary representation of n.
%H Rémy Sigrist, <a href="/A342698/b342698.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) + A342700(n) = A003817(n).
%F a(n) = n iff n belongs to A342699.
%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 1 1 1
%e 2 1 10 1
%e 3 3 11 11
%e 4 0 100 0
%e 5 7 101 111
%e 6 7 110 111
%e 7 7 111 111
%e 8 0 1000 0
%e 9 9 1001 1001
%e 10 5 1010 101
%e 11 15 1011 1111
%e 12 12 1100 1100
%e 13 15 1101 1111
%e 14 15 1110 1111
%e 15 15 1111 1111
%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))>=2) * 2^k)
%Y Cf. A003817, A342697, A342699 (fixed points), A342700.
%K nonn,base
%O 0,4
%A _Rémy Sigrist_, Mar 18 2021
|
