A342698 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)).

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, 31, 28, 31, 31, 31, 0, 33, 1, 35, 0, 35, 7, 39, 16, 49, 21, 55, 28, 63, 31, 63, 48, 49, 49, 51, 56, 59, 63, 63, 56, 57, 61, 63, 60, 63, 63, 63, 0, 65, 1, 67, 0, 67, 7

Offset: 0

Author

Rémy Sigrist, Mar 18 2021

Keywords

• nonn
• base

Comments

This sequence is a variant of A342697; here we deal with bit triples in a "cyclic" binary representation of n.

Examples

			The first terms, in decimal and in binary, are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     1      10          1
   3     3      11         11
   4     0     100          0
   5     7     101        111
   6     7     110        111
   7     7     111        111
   8     0    1000          0
   9     9    1001       1001
  10     5    1010        101
  11    15    1011       1111
  12    12    1100       1100
  13    15    1101       1111
  14    15    1110       1111
  15    15    1111       1111
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8192
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A003817, A342697, A342699 (fixed points), A342700.

Programs

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)

Formula

a(n) + A342700(n) = A003817(n).

a(n) = n iff n belongs to A342699.