A342698 - OEIS

%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