A065712 Number of 1's in decimal expansion of 2^n.

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

Offset: 0

Author

Benoit Cloitre, Dec 04 2001

Keywords

• nonn
• base

Comments

I conjecture that any value x = 0, 1, 2, ... occurs only a finite number of times N(x) = 26, 34, 30, 40, 26, 33, 39, 30, 30, 30, 38, ... in this sequence, for the last time at well defined indices i(x) = 91, 152, 185, 412, 245, 505, 346, 422, 499, 565, 529, 575, ... - M. F. Hasler, Jul 09 2025

Examples

			2^17 = 131072 so a(17) = 2.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A027870 (0's), A065710 (2's), A065714 (3's), A065715 (4's), A065716 (5's), A065717 (6's), A065718 (7's), A065719 (8's), A065744 (9's).

Indices of zeros are listed in A035057 (2^n does not contain the digit 1).

Programs

Mathematica

Table[ Count[ IntegerDigits[2^n], 1], {n, 0, 100} ]
Table[DigitCount[2^n,10,1],{n,0,120}] (* Harvey P. Dale, Aug 15 2014 *)

PARI

a(n) = #select(x->(x==1), digits(2^n)); \\ Michel Marcus, Jun 15 2018

Python

def A065712(n):
    return str(2**n).count('1') # Chai Wah Wu, Feb 14 2020

Extensions

More terms from Robert G. Wilson v, Dec 07 2001