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A153142
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Permutation of nonnegative integers: A059893-conjugate of A153152.
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19
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0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 14, 15, 10, 11, 9, 8, 24, 25, 26, 27, 28, 29, 30, 31, 20, 21, 22, 23, 18, 19, 17, 16, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 40, 41, 42, 43, 44, 45, 46, 47, 36, 37, 38, 39, 34, 35, 33, 32, 96, 97, 98, 99, 100, 101, 102
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OFFSET
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0,3
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COMMENTS
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This sequence can be also obtained by starting complementing n's binary expansion from the second most significant bit, continuing towards lsb-end until the first 0-bit is reached, which is the last bit to be complemented.
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LINKS
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EXAMPLE
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29 = 11101 in binary. By complementing bits in (zero-based) positions 3, 2 and 1 we get 10011 in binary, which is 19 in decimal, thus a(29)=19.
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PROG
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(MIT/GNU Scheme) (define (a153142 n) (if (< n 2) n (let loop ((maskbit (a072376 n)) (z n)) (cond ((zero? maskbit) z) ((zero? (modulo (floor->exact (/ n maskbit)) 2)) (+ z maskbit)) (else (loop (floor->exact (/ maskbit 2)) (- z maskbit)))))))
(Python)
def ok(n): return n&(n - 1)==0
def a153152(n): return n if n<2 else (n + 1)/2 if ok(n + 1) else n + 1
def A(n): return (int(bin(n)[2:][::-1], 2) - 1)/2
def msb(n): return n if n<3 else msb(n/2)*2
def a059893(n): return A(n) + msb(n)
def a(n): return 0 if n==0 else a059893(a153152(a059893(n))) # Indranil Ghosh, Jun 09 2017
(R)
maxlevel <- 5 # by choice
a <- 1
for(m in 1:maxlevel){
a[2^(m+1) - 1] <- 2^m
a[2^(m+1) - 2] <- 2^m + 1
for (k in 0:(2^m-2)){
a[2^(m+1) + 2*k ] <- 2*a[2^m + k]
a[2^(m+1) + 2*k + 1] <- 2*a[2^m + k] + 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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