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A374664 Nonnegative numbers whose binary expansion has no ones in common with some of its cyclic shifts.

%I A374664 #11 Jul 24 2024 09:00:09
%S A374664 0,2,4,8,9,10,12,16,17,18,20,24,32,33,34,35,36,40,42,48,49,56,64,65,
%T A374664 66,67,68,72,73,74,76,80,82,84,96,97,100,112,128,129,130,131,132,133,
%U A374664 134,135,136,137,138,140,144,145,146,148,150,152,153,160,161,162
%N A374664 Nonnegative numbers whose binary expansion has no ones in common with some of its cyclic shifts.
%C A374664 Leading zeros in binary expansions are ignored.
%C A374664 All positive terms belong to A072602.
%C A374664 A number k belongs to the sequence iff A001196(k) belongs to the sequence.
%H A374664 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e A374664 The first terms, with their binary expansion and an appropriate cyclic shift, are:
%e A374664   n   a(n)  bin(a(n))  cyc
%e A374664   --  ----  ---------  ------
%e A374664    1     0          0       0
%e A374664    2     2         10      01
%e A374664    3     4        100     001
%e A374664    4     8       1000    0001
%e A374664    5     9       1001    0110
%e A374664    6    10       1010    0101
%e A374664    7    12       1100    0011
%e A374664    8    16      10000   00001
%e A374664    9    17      10001   00110
%e A374664   10    18      10010   00101
%e A374664   11    20      10100   01001
%e A374664   12    24      11000   00011
%e A374664   13    32     100000  000001
%e A374664   14    33     100001  000110
%e A374664   15    34     100010  000101
%e A374664   16    35     100011  011100
%o A374664 (PARI) is(n) = { my (x = max(exponent(n), 0), s = n); for (i = 0, x, s = (s >> 1) + if (s%2, 2^x, 0); if (bitand(s, n)==0, return (1););); return (0); }
%Y A374664 Cf. A001196, A006257, A038572, A072602, A140900, A374712.
%K A374664 nonn,base,easy
%O A374664 1,2
%A A374664 _Rémy Sigrist_, Jul 15 2024