A378299 Read the binary representation of n from the most to least significant bit then perform a cumulative XOR and store by reading from least to most significant bit.

0, 1, 1, 2, 1, 6, 2, 5, 1, 14, 6, 9, 2, 13, 5, 10, 1, 30, 14, 17, 6, 25, 9, 22, 2, 29, 13, 18, 5, 26, 10, 21, 1, 62, 30, 33, 14, 49, 17, 46, 6, 57, 25, 38, 9, 54, 22, 41, 2, 61, 29, 34, 13, 50, 18, 45, 5, 58, 26, 37, 10, 53, 21, 42, 1, 126, 62, 65, 30, 97, 33, 94

Offset

0,4

Comments

a(n) is Gray-coded into the reversed binary representation of n.

Fixed points are 0 and f(n) = 8*f(n-1) + 5 with f(1)=1 or f(n) = (1/14)*(3*(2^(3*n))-10) for n >= 1 (cf. A380001).

Links

Paolo Xausa, Table of n, a(n) for n = 0..16383

Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^20.

Michael De Vlieger, Fan style binary tree showing a(n), n = 0..2^13-1, with a color function showing a(n) according to floor(log_2(a(n))).

Index entries for sequences related to binary expansion of n

Formula

a(n) = A006068(A030101(n)).

a(A000079(n)) = 1.

a(A007283(n)) = 2.

a(A000225(n)) = A000975(n).

a(A000051(n)) = A095121(n).

Example

For n = 75 a(75) = 78 because:
75 in base 2 is 1001011 and in base 2:
  m      | x = x XOR (m AND 1) | o
---------+---------------------+----------
1001011  | 1 = 0 XOR 1         |       1
100101   | 0 = 1 XOR 1         |      10
10010    | 0 = 0 XOR 0         |     100
1001     | 1 = 0 XOR 1         |    1001
100      | 1 = 1 XOR 0         |   10011
10       | 1 = 1 XOR 0         |  100111
1        | 0 = 1 XOR 1         | 1001110
And 1001110 in base 10: 78

Mathematica

A378299[n_] := FromDigits[FoldList[BitXor, 0, Reverse[IntegerDigits[n, 2]]], 2];
Array[A378299, 100, 0] (* Paolo Xausa, Dec 13 2024 *)

Prog

(Python)
def a(n):
  m, x, o = n, 0, 0
  while m > 0:
    x ^= (m & 1)
    o <<= 1
    o |= x
    m >>=1
  return o
print([a(n) for n in range(0, 71)])

Crossrefs

Cf. A000079, A000225, A000051, A000975, A007283, A006068, A030101, A095121.

Cf. A380001 (fixed points).

Sequence in context: A198870 A359273 A372909 * A365048 A050457 A195441

Adjacent sequences: A378296 A378297 A378298 * A378300 A378301 A378302

Keyword

nonn,base,look

Author

Darío Clavijo, Nov 22 2024

Status

approved