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

0,18

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

Links

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

Example

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

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 *)

Prog

(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

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).

Sequence in context: A024359 A354512 A088705 * A153172 A242498 A321927

Adjacent sequences: A065709 A065710 A065711 * A065713 A065714 A065715

Keyword

nonn,base

Author

Benoit Cloitre, Dec 04 2001

Extensions

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

Status

approved