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A309952 XOR contraction of binary representation of n. 1
0, 1, 1, 0, 2, 3, 3, 2, 2, 3, 3, 2, 0, 1, 1, 0, 4, 5, 5, 4, 6, 7, 7, 6, 6, 7, 7, 6, 4, 5, 5, 4, 4, 5, 5, 4, 6, 7, 7, 6, 6, 7, 7, 6, 4, 5, 5, 4, 0, 1, 1, 0, 2, 3, 3, 2, 2, 3, 3, 2, 0, 1, 1, 0, 8, 9, 9, 8, 10, 11, 11, 10, 10, 11, 11, 10, 8, 9, 9, 8, 12, 13, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

To calculate a(n) write down the binary representation of n. Organize the digits in pairs and calculate the xor of these pairs. The result is a(n) in binary.

Conjecture: The index of the first occurrence of k in a is A000695(k). - Ivan N. Ianakiev, Aug 26 2019

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..16383

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = A292371(n) + A292372(n). - Rémy Sigrist, Aug 25 2019

a(0) = 0, a(4n) = 2*a(n), a(4n+1) = 2*a(n)+1, a(4n+2) = 2*a(n)+1, a(4n+3) = 2*a(n). - Florian Lang, Aug 26 2019

EXAMPLE

For n=19 we have the binary representation 10011 = 01 00 11. Calculating the xor of the pairs gives 1 0 0 which is 4 in binary and therefore a(19) = 4.

MAPLE

a:= n-> `if`(n=0, 0, (r-> 2*a((n-r)/4) +r*(3-r)/2)(irem(n, 4))):

seq(a(n), n=0..100);  # Alois P. Heinz, Aug 26 2019

PROG

(Python)

def a(n):

    n = [int(k) for k in bin(n)[2:]]

    if len(n) % 2 != 0:

        n = [0] + n

    result = []

    for i in range(0, len(n), 2):

        result.append(n[i] ^ n[i+1]) #xor

    return int("".join([str(k) for k in result]), 2)

(PARI) a(n) = {my(b = Vecrev(binary(n)), nb = #b\2, val = fromdigits(Vecrev(vector(nb, i, bitxor(b[2*i-1], b[2*i]))), 2)); if (#b % 2, val += 2^nb); val; } \\ Michel Marcus, Aug 26 2019

CROSSREFS

Cf. A000695, A292371, A292372, A292373.

Sequence in context: A096838 A096007 A269043 * A059252 A251619 A030620

Adjacent sequences:  A309949 A309950 A309951 * A309953 A309954 A309955

KEYWORD

base,easy,look,nonn

AUTHOR

Florian Lang, Aug 24 2019

STATUS

approved

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Last modified June 14 08:31 EDT 2021. Contains 345018 sequences. (Running on oeis4.)