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A064706
Square of permutation defined by A003188.
10
0, 1, 2, 3, 5, 4, 7, 6, 10, 11, 8, 9, 15, 14, 13, 12, 20, 21, 22, 23, 17, 16, 19, 18, 30, 31, 28, 29, 27, 26, 25, 24, 40, 41, 42, 43, 45, 44, 47, 46, 34, 35, 32, 33, 39, 38, 37, 36, 60, 61, 62, 63, 57, 56, 59, 58, 54, 55, 52, 53, 51, 50, 49, 48, 80, 81, 82, 83, 85, 84, 87, 86
OFFSET
0,3
COMMENTS
Inverse of sequence A064707 considered as a permutation of the nonnegative integers.
Not the same as A100282: a(n) = A100282(n) = A100280(A100280(n)) only for n < 64. - Reinhard Zumkeller, Nov 11 2004
FORMULA
a(n) = A003188(A003188(n)).
a(n) = n XOR floor(n/4), where XOR is binary exclusive OR. - Paul D. Hanna, Oct 25 2004
a(n) = A233280(A180201(n)), n > 0. - Yosu Yurramendi, Apr 05 2017
a(n) = A000695(A003188(A059905(n))) + 2*A000695(A003188(A059906(n))). - Antti Karttunen, Apr 14 2018
MATHEMATICA
Array[BitXor[#, Floor[#/4]] &, 72, 0] (* Michael De Vlieger, Apr 14 2018 *)
PROG
(MATLAB) A = 1; for i = 1:7 B = A(end:-1:1); A = [A (B + length(A))]; end A(A) - 1
(PARI) a(n)=bitxor(n, n\4)
(PARI) { for (n=0, 1000, write("b064706.txt", n, " ", bitxor(n, n\4)) ) } \\ Harry J. Smith, Sep 22 2009
(R)
maxn <- 63 # by choice
b <- c(1, 0, 0)
for(n in 4:maxn) b[n] <- b[n-1] - b[n-2] + b[n-3]
# c(1, b) is A133872
a <- 1
for(n in 1:maxn) {
a[2*n ] <- 2*a[n] + 1 - b[n]
a[2*n+1] <- 2*a[n] + b[n]
}
(a <- c(0, a))
# Yosu Yurramendi, Oct 25 2020
(Python)
def A064706(n): return n^ n>>2 # Chai Wah Wu, Jun 29 2022
CROSSREFS
Cf. A064707 (inverse), A165211 (mod 2).
Cf. also A054238, A163233, A302846.
Sequence in context: A101212 A232641 A258746 * A100282 A100281 A064707
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Oct 13 2001
EXTENSIONS
More terms from David Wasserman, Aug 02 2002
STATUS
approved