A038572 a(n) = n rotated one binary place to the right.

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

Cf. A006257, A088146.

Sequence in context: A071018 A144559 A155114 * A334667 A245676 A341516

Adjacent sequences: A038569 A038570 A038571 * A038573 A038574 A038575

Keyword

easy,base,nonn,nice

Author

Marc LeBrun

Status

approved