A027870 Number of zeros in 2^n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 3, 1, 1, 1, 1, 1, 0, 1, 0, 2, 3, 2, 2, 2, 1, 1, 2, 2, 3, 2, 2, 2, 1, 1, 0, 1, 3, 3, 1, 0, 1, 1, 1, 0, 0, 2, 4, 2, 0, 2, 3, 1, 1, 0, 3, 5, 3, 3, 4, 2, 3, 4, 1, 1, 4, 5, 5, 6, 6, 7, 5, 5

Offset

0,43

Comments

a(A007377(n)) = 0; A224782(n) <= a(n). - Reinhard Zumkeller, Apr 30 2013

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000 (first 1001 terms from Harry J. Smith)

Formula

a(n) = A055641(A000079(n)). - Reinhard Zumkeller, Apr 30 2013

Example

2^31 = 2147483648 so a(31) = 0 and 2^42 = 4398046511104 so a(42) = 2.

Mathematica

Table[ Count[ IntegerDigits[2^n], 0], {n, 0, 100} ]
DigitCount[2^Range[0, 110], 10, 0] (* Harvey P. Dale, Nov 20 2011 *)

Prog

(PARI) Count(x, d)= { local(c=0, f); while (x>9, f=x-10*(x\10); if (f==d, c++); x\=10); if (x==d, c++); return(c) }
{ for (n=0, 1000, a=Count(2^n, 0); write("b027870.txt", n, " ", a) ) } \\ Harry J. Smith, Oct 27 2009
(PARI) A027870(n)=#select(d->!d, digits(2^n)) \\ M. F. Hasler, Jun 14 2018
(Haskell) a027870 = a055641 . a000079  -- Reinhard Zumkeller, Apr 30 2013
(Python)
def A027870(n):
    return str(2**n).count('0') # Chai Wah Wu, Feb 14 2020

Crossrefs

Cf. A007377, 1's A065712, 2's A065710, 3's A065714, 4's A065715, 5's A065716, 6's A065717, 7's A065718, 8's A065719, 9's A065744.

Cf. A031146: index of first appearence of n in this sequence.

Cf. A305932: table with n in row a(n).

Sequence in context: A352195 A321895 A321899 * A357526 A070077 A337200

Adjacent sequences: A027867 A027868 A027869 * A027871 A027872 A027873

Keyword

nonn,base

Author

N. J. A. Sloane

Extensions

a(99)-a(104) from Harry J. Smith, Oct 27 2009

Status

approved