A123384 Number of bits in binary expansion of 10^n.

1, 4, 7, 10, 14, 17, 20, 24, 27, 30, 34, 37, 40, 44, 47, 50, 54, 57, 60, 64, 67, 70, 74, 77, 80, 84, 87, 90, 94, 97, 100, 103, 107, 110, 113, 117, 120, 123, 127, 130, 133, 137, 140, 143, 147, 150, 153, 157, 160, 163, 167, 170, 173, 177, 180, 183, 187, 190, 193, 196

Offset: 0

Author

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

Keywords

• base
• nonn

Comments

Number of powers of 2 less than or equal to 10^n. - Peter Munn, Nov 13 2019

Examples

			a(3)=10 because 10^3 = 1111101000_2.
10^1 = 10 = 1010_2 has 4 digits.
		

Crossrefs

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

Row 1 of A253635.

Programs

Maple

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

Mathematica

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

Formula

a(n) = 1 + floor(n/A007524) = 1 + floor(n/log_10(2)). - R. J. Mathar, Nov 12 2006

a(n) = 1 + A066343(n). - R. J. Mathar, Mar 02 2007

a(n) = A067497(n) for n >= 1. - Georg Fischer, Nov 02 2018

Extensions

More terms from Emeric Deutsch, Mar 26 2007