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A224915 a(n) = Sum_{k=0..n} n XOR k where XOR is the bitwise logical exclusive-or operator. 3
0, 1, 5, 6, 22, 23, 27, 28, 92, 93, 97, 98, 114, 115, 119, 120, 376, 377, 381, 382, 398, 399, 403, 404, 468, 469, 473, 474, 490, 491, 495, 496, 1520, 1521, 1525, 1526, 1542, 1543, 1547, 1548, 1612, 1613, 1617, 1618, 1634, 1635, 1639, 1640, 1896, 1897, 1901, 1902, 1918 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = Sum_{j=1..n} 4^(v_2(j)), where v_2(j) is the exponent of highest power of 2 dividing j. - Ridouane Oudra, Jun 08 2019

a(n) = n + 3*Sum_{j=1..floor(log_2(n))} 4^(j-1)*floor(n/2^j), for n>=1. - Ridouane Oudra, Dec 09 2020

EXAMPLE

a(2) = (0 xor 2) + (1 xor 2) = 2 + 3 = 5.

MAPLE

read("transforms"):

A051933 := proc(n, k)

    XORnos(n, k) ;

end proc:

A224915 := proc(n)

    add(A051933(n, k), k=0..n) ;

end proc: # R. J. Mathar, Apr 26 2013

# second Maple program:

with(MmaTranslator[Mma]):

seq(add(BitXor(n, i), i=0..n), n=0..60); # Ridouane Oudra, Dec 09 2020

MATHEMATICA

Array[Sum[BitXor[#, k], {k, 0, #}] &, 53, 0] (* Michael De Vlieger, Dec 09 2020 *)

PROG

(Python)

for n in range(99):

    s = 0

    for k in range(n):  s += n ^ k

    print s,

(PARI) a(n) = sum(k=0, n, bitxor(n, k)); \\ Michel Marcus, Jun 08 2019

CROSSREFS

Cf. A004125, A222423, row sums of A051933.

Sequence in context: A132796 A006492 A110344 * A135301 A294175 A192917

Adjacent sequences:  A224912 A224913 A224914 * A224916 A224917 A224918

KEYWORD

nonn,easy

AUTHOR

Alex Ratushnyak, Apr 19 2013

STATUS

approved

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Last modified February 26 18:42 EST 2021. Contains 341632 sequences. (Running on oeis4.)