(Translated by https://www.hiragana.jp/)
A038572 - OEIS
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A038572
a(n) = n rotated one binary place to the right.
31
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
OFFSET
0,4
COMMENTS
Iterating a(n), a(a(n)), ... eventually leads to 2^A000120(n) - 1. - Franklin T. Adams-Watters, Apr 09 2010
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..20000 (first 1024 terms from T. D. Noe)
FORMULA
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
EXAMPLE
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
MAPLE
A038572 := proc(n)
convert(n, base, 2) ;
ListTools[Rotate](%, 1) ;
add( op(i, %)*2^(i-1), i=1..nops(%)) ;
end proc: # R. J. Mathar, May 20 2016
MATHEMATICA
Table[ FromDigits[ RotateRight[ IntegerDigits[n, 2]], 2], {n, 0, 80}] (* Robert G. Wilson v *)
PROG
(Haskell)
a038572 0 = 0
a038572 n = a053645 n * m + n' where (n', m) = divMod n 2
-- Reinhard Zumkeller, Dec 03 2012
(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)
def A038572(n):
x = bin(n)[2:]
return int(x[-1]+x[:-1], 2) # Indranil Ghosh, Jan 21 2017
(Python)
def A038572(n): return (n>>1)+(1<<n.bit_length()-1 if n&1 else 0) # Chai Wah Wu, Jan 22 2023
CROSSREFS
Sequence in context: A071018 A144559 A155114 * A334667 A245676 A341516
KEYWORD
easy,base,nonn,nice
AUTHOR
STATUS
approved