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

%I A065744 #34 Jul 12 2025 18:54:35
%S A065744 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,
%T A065744 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,
%U A065744 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
%N A065744 Number of 9's in the decimal expansion of 2^n.
%C A065744 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
%H A065744 Harry J. Smith, <a href="/A065744/b065744.txt">Table of n, a(n) for n = 0..1000</a>
%e A065744 2^12 = 4096 so a(12)=1.
%t A065744 Table[ Count[ IntegerDigits[2^n], 9], {n, 0, 100} ]
%o A065744 (PARI)
%o A065744 Count(x,d)={ #select(t->t==d, digits(x)) }
%o A065744 a(n) = Count(2^n, 9) \\ _Harry J. Smith_, Oct 27 2009
%o A065744 (Python)
%o A065744 def A065744(n):
%o A065744     return str(2**n).count('9')  # _Chai Wah Wu_, Feb 14 2020
%Y A065744 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).
%Y A065744 Cf. A035064 (2^n has no digit 9).
%K A065744 nonn,base
%O A065744 0,33
%A A065744 _Benoit Cloitre_, Dec 04 2001
%E A065744 More terms from _Robert G. Wilson v_, Dec 07 2001