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A180094 Number of steps to reach 0 or 1, starting with n and applying the map k -> (number of 1's in binary expansion of k) repeatedly. 3
0, 0, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 2, 1, 2, 2, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 3, 2, 2, 3, 2, 3, 3, 3, 1, 2, 2, 3, 2, 3, 3, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 3, 2, 3, 2, 2, 3, 3, 2, 2, 3, 2, 3, 3, 3, 2, 3, 3, 2, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The number of 1's in binary expansion of n is called the binary weight (or Hamming weight) of n, A000120(n).

a(n)=0 for n=0 and n=1;  a(n)=1 for powers of 2.

Records appear for n = 2, 3, 7, 127=2^7-1, 2^127-1, ... (terms of A007013).

It appears that the indices of the even terms for n>0 are sequence A075311.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

MAPLE

a:= n-> `if`(n<2, 0, 1 + a(add(i, i=convert(n, base, 2)))):

seq(a(n), n=0..100);  # Alois P. Heinz, Jan 15 2011

MATHEMATICA

Table[Length[NestWhileList[DigitCount[#, 2, 1]&, n, #>1&]]-1, {n, 0, 100}] (* Harvey P. Dale, Jul 27 2012 *)

PROG

(PARI)

bitcount(x)=

{ /* Return Hamming weight of x, i.e. A000120(x) */

    local(p);  p = 0;

    while ( x, p+=bitand(x, 1); x>>=1; );

    return( p );

}

X(n)=

{ /* Return how many iterations of bitcount() are needed to reach 0 or 1 */

    if ( n<=1, return(0) );

    return( 1+X(bitcount(n)) );

}

{ for (n=0, 100, print1(X(n), ", ") ); } /* print terms of sequence */

(MAGMA)

Countbits:=func< n | &+Intseq(n, 2) >;

StepsTo01:=function(n); s:=0; k:=n; while k gt 1 do k:=Countbits(k); s+:=1; end while; return s; end function;

[ StepsTo01(n): n in [0..105] ]; // Klaus Brockhaus, Jan 15 2011

(Haskell)

a180094 n = snd $ until ((< 2) . fst) (\(x, c) -> (a000120 x, c+1)) (n, 0)

-- Reinhard Zumkeller, Apr 22 2011

CROSSREFS

Cf. A000120, A072086.

One less than A078627.

Sequence in context: A179868 A104232 A072086 * A333870 A103748 A104231

Adjacent sequences:  A180091 A180092 A180093 * A180095 A180096 A180097

KEYWORD

nonn

AUTHOR

Joerg Arndt, Jan 15 2011

STATUS

approved

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Last modified September 30 15:55 EDT 2020. Contains 337439 sequences. (Running on oeis4.)