A065744 Number of 9's in the decimal expansion of 2^n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 3, 3, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 0, 0, 0, 1, 3, 3, 2, 3, 5, 3, 3, 3, 0, 0, 0, 2, 3, 1, 1, 1, 2, 2, 3, 3, 2, 1, 0, 2, 5, 2, 3, 2, 0, 2, 2, 3, 3, 1, 4, 3, 2, 1, 2, 2, 4, 4, 2, 6, 8, 3, 3, 3, 1, 1, 0, 2

Offset: 0

Author

Benoit Cloitre, Dec 04 2001

Keywords

• nonn
• base

Comments

See A035064 for the indices of zeros. I conjecture that any value x = 0, 1, 2, ... occurs only a finite number of times N(x) = 37, 27, 36, 46, 20, 31, 32, 30, 46, 29, 22, ... in this sequence, for the last time at well defined indices i(x) = 108, 197, 296, 277, 278, 315, 379, 555, 503, 504, 539, 696, 667, ... - M. F. Hasler, Jul 09 2025

Examples

			2^12 = 4096 so a(12)=1.
		

Links

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

Crossrefs

Similar for other digits: A027870 (0's), A065712 (1's), A065710 (2's), A065714 (3's), A065715 (4's), A065716 (5's), A065717 (6's), A065718 (7's), A065719 (8's).

Cf. A035064 (2^n has no digit 9).

Programs

Mathematica

Table[ Count[ IntegerDigits[2^n], 9], {n, 0, 100} ]

PARI

Count(x,d)={ #select(t->t==d, digits(x)) }
a(n) = Count(2^n, 9) \\ Harry J. Smith, Oct 27 2009

Python

def A065744(n):
    return str(2**n).count('9')  # Chai Wah Wu, Feb 14 2020

Extensions

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