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

0, 2, 4, 8, 9, 10, 12, 16, 17, 18, 20, 24, 32, 33, 34, 35, 36, 40, 42, 48, 49, 56, 64, 65, 66, 67, 68, 72, 73, 74, 76, 80, 82, 84, 96, 97, 100, 112, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 140, 144, 145, 146, 148, 150, 152, 153, 160, 161, 162

Offset: 1

Author

Rémy Sigrist, Jul 15 2024

Keywords

• nonn
• base
• easy

Comments

Leading zeros in binary expansions are ignored.

All positive terms belong to A072602.

A number k belongs to the sequence iff A001196(k) belongs to the sequence.

Examples

			The first terms, with their binary expansion and an appropriate cyclic shift, are:
  n   a(n)  bin(a(n))  cyc
  --  ----  ---------  ------
   1     0          0       0
   2     2         10      01
   3     4        100     001
   4     8       1000    0001
   5     9       1001    0110
   6    10       1010    0101
   7    12       1100    0011
   8    16      10000   00001
   9    17      10001   00110
  10    18      10010   00101
  11    20      10100   01001
  12    24      11000   00011
  13    32     100000  000001
  14    33     100001  000110
  15    34     100010  000101
  16    35     100011  011100
		

Links

• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A001196, A006257, A038572, A072602, A140900, A374712.

Programs

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); }