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Number of bits in binary expansion of 10^n.
13

%I #28 Aug 31 2024 11:08:12

%S 1,4,7,10,14,17,20,24,27,30,34,37,40,44,47,50,54,57,60,64,67,70,74,77,

%T 80,84,87,90,94,97,100,103,107,110,113,117,120,123,127,130,133,137,

%U 140,143,147,150,153,157,160,163,167,170,173,177,180,183,187,190,193,196

%N Number of bits in binary expansion of 10^n.

%C Number of powers of 2 less than or equal to 10^n. - _Peter Munn_, Nov 13 2019

%F a(n) = 1 + floor(n/A007524) = 1 + floor(n/log_10(2)). - _R. J. Mathar_, Nov 12 2006

%F a(n) = 1 + A066343(n). - _R. J. Mathar_, Mar 02 2007

%F a(n) = A067497(n) for n >= 1. - _Georg Fischer_, Nov 02 2018

%e a(3)=10 because 10^3 = 1111101000_2.

%e 10^1 = 10 = 1010_2 has 4 digits.

%p A007524 := log[10](2.0) ; for n from 0 to 40 do printf("%d,", 1+floor(n/A007524)) ; od: # _R. J. Mathar_, Nov 12 2006

%p a:=n->nops(convert(10^n,base,2)): seq(a(n),n=0..70); # _Emeric Deutsch_, Mar 26 2007

%t a[n_]:=1 + Floor[n/Log10[2]]; Array[a,60,0] (* _Stefano Spezia_, Aug 31 2024 *)

%Y Cf. A000079, A007524, A011557, A066343, A067497.

%Y Row 1 of A253635.

%K base,nonn

%O 0,2

%A Andrew Caldwell (spongebobpj(AT)yahoo.com), Nov 09 2006

%E More terms from _Emeric Deutsch_, Mar 26 2007