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A038572
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a(n) = n rotated one binary place to the right.
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30
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0, 1, 1, 3, 2, 6, 3, 7, 4, 12, 5, 13, 6, 14, 7, 15, 8, 24, 9, 25, 10, 26, 11, 27, 12, 28, 13, 29, 14, 30, 15, 31, 16, 48, 17, 49, 18, 50, 19, 51, 20, 52, 21, 53, 22, 54, 23, 55, 24, 56, 25, 57, 26, 58, 27, 59, 28, 60, 29, 61, 30, 62, 31, 63, 32, 96, 33, 97, 34, 98, 35, 99, 36, 100
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listen;
history;
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internal format)
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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a(n) = A053645(n) * A000035(n) + A004526(n) = most significant bit(n) * least significant bit(n) + floor(n/2).
a(0)=0, a(1)=1, a(2n) = n, a(2n+1) = 2a(n) + 2a(n+1) - n. - Ralf Stephan, Oct 24 2003
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EXAMPLE
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For n = 35, 35_10 = 100011_2, which after rotating one binary place to the right becomes 110001. Now, 110001_2 = 49_10. So, a(35) = 49. - Indranil Ghosh, Jan 21 2017
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MAPLE
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convert(n, base, 2) ;
ListTools[Rotate](%, 1) ;
add( op(i, %)*2^(i-1), i=1..nops(%)) ;
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MATHEMATICA
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Table[ FromDigits[ RotateRight[ IntegerDigits[n, 2]], 2], {n, 0, 80}] (* Robert G. Wilson v *)
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PROG
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(Haskell)
a038572 0 = 0
a038572 n = a053645 n * m + n' where (n', m) = divMod n 2
(PARI) a(n)=if(n<2, return(n)); my(d=binary(n)); fromdigits(concat(d[#d], d[1..#d-1]), 2) \\ Charles R Greathouse IV, Sep 02 2015
(Python)
x = bin(n)[2:]
(Python)
def A038572(n): return (n>>1)+(1<<n.bit_length()-1 if n&1 else 0) # Chai Wah Wu, Jan 22 2023
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CROSSREFS
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KEYWORD
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easy,base,nonn,nice
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AUTHOR
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STATUS
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approved
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