A344259 For any number n with binary expansion (b(1), ..., b(k)), the binary expansion of a(n) is (b(1), ..., b(ceiling(k/2))).

0, 1, 1, 1, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10

Offset: 0

Author

Rémy Sigrist, May 13 2021

Keywords

• nonn
• base
• easy

Comments

Leading zeros are ignored.

Examples

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8191
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A006995, A020330, A162751, A344220.

Programs

Mathematica

Array[FromDigits[First@Partition[l=IntegerDigits[#,2],Ceiling[Length@l/2]],2]&,100,0] (* Giorgos Kalogeropoulos, May 14 2021 *)

PARI

a(n) = n\2^(#binary(n)\2)

Python

def a(n): b = bin(n)[2:]; return int(b[:(len(b)+1)//2], 2)
print([a(n) for n in range(85)]) # Michael S. Branicky, May 14 2021

Formula

a(A020330(n)) = n.

a(A006995(n+1)) = A162751(n).

a(n XOR A344220(n)) = a(n) (where XOR denotes the bitwise XOR operator).