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A153154
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Permutation of natural numbers: A059893-conjugate of A006068.
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5
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0, 1, 3, 2, 7, 4, 5, 6, 15, 8, 9, 14, 11, 12, 13, 10, 31, 16, 17, 30, 19, 28, 29, 18, 23, 24, 25, 22, 27, 20, 21, 26, 63, 32, 33, 62, 35, 60, 61, 34, 39, 56, 57, 38, 59, 36, 37, 58, 47, 48, 49, 46, 51, 44, 45, 50, 55, 40, 41, 54, 43, 52, 53, 42, 127, 64, 65, 126, 67, 124
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(1) = 1, for all n > 0 a(2*n) = 2*a(n) + 1, a(2*n+1) = 2*a(A065190(n)).
a(1) = 1, a(2) = 3, a(3) = 2, for all n > 1 a(2*n) = 2*a(n) + 1, and if n even a(2*n+1) = 2*a(n+1), else a(2*n+1) = 2*a(n-1).
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PROG
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(R)
maxn <- 63 # by choice
a <- c(1, 3, 2)
#
for(n in 2:maxn){
a[2*n] <- 2*a[n] + 1
if(n%%2==0) a[2*n+1] <- 2*a[n+1]
else a[2*n+1] <- 2*a[n-1]
}
(a <- c(0, a))
(R)
# Given n, compute a(n) by taking into account the binary representation of n
maxblock <- 8 # by choice
a <- c(1, 3, 2)
for(n in 4:2^maxblock){
ones <- which(as.integer(intToBits(n)) == 1)
nbit <- as.integer(intToBits(n))[1:tail(ones, n = 1)]
anbit <- nbit
for(i in 2:(length(anbit) - 1))
anbit[i] <- bitwXor(anbit[i], anbit[i - 1]) # ?bitwXor
anbit[0:(length(anbit) - 1)] <- 1 - anbit[0:(length(anbit) - 1)]
a <- c(a, sum(anbit*2^(0:(length(anbit) - 1))))
}
(a <- c(0, a))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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