A136480 Number of trailing equal digits in binary representation of n.

1, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 5, 5, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 6, 6, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 4, 4, 1, 1, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 1, 1, 5, 5, 1, 1, 2, 2, 1, 1, 3, 3

Offset

0,4

Comments

a(even) = number of trailing binary zeros;

a(odd) = number of trailing binary ones.

For n>0, power of 2 associated with n^2 + n, e.g. n=4 gives 20, so a(4)=2. - Jon Perry, Sep 12 2014

Links

James Spahlinger, Table of n, a(n) for n = 0..10000

Francis Laclé, 2-adic parity explorations of the 3n+ 1 problem, hal-03201180v2 [cs.DM], 2021.

Index entries for sequences related to binary expansion of n

Formula

a(n) = A050603(n-1) for n>0;

a(2*n + n mod 2) = a(n) + 1.

For n>0: a(n) = A007814(n + n mod 2).

Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=0..m} a(k) = 2. - Amiram Eldar, Sep 15 2022

a(n) = A007814(A002378(n)), n>0. - R. J. Mathar, Mar 20 2023

Maple

A136480 := proc(n)
    if n = 0 then
        1;
    else
        A007814(n*(n+1)) ;
    end if;
end proc:
seq( A136480(n), n=0..80) ; # R. J. Mathar, Mar 20 2023

Mathematica

Length[Last[Split[IntegerDigits[#, 2]]]]&/@Range[0, 140]  (* Harvey P. Dale, Mar 31 2011 *)

Prog

(PARI) a(n)=if (n, valuation(n+n%2, 2), 1) \\ Charles R Greathouse IV, Oct 14 2013
(Haskell)
a136480 0 = 1
a136480 n = a007814 $ n + mod n 2  -- Reinhard Zumkeller, Jul 22 2014
(JavaScript)
for (n=1; n<120; n++) {
m=n*n+n;
c=0;
while (m%2==0) {m/=2; c++; }
document.write(c+", ");
}  // Jon Perry, Sep 12 2014
(Python)
def A136480(n): return (~(m:=n+(n&1))& m-1).bit_length() # Chai Wah Wu, Jul 08 2022

Crossrefs

Cf. A007814, A050603, A094267, A163575, A001511, A039963 (parity).

Sequence in context: A064894 A003638 A094267 * A050603 A286554 A352784

Adjacent sequences: A136477 A136478 A136479 * A136481 A136482 A136483

Keyword

nonn,base,easy

Author

Reinhard Zumkeller, Dec 31 2007

Status

approved