A125122 First differences of A034888.

0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0

Offset: 0

Author

Paolo P. Lava and Giorgio Balzarotti, Jan 10 2007

Keywords

• easy
• nonn
• base

Comments

This sequence is not periodic because log(3)/log(10) is an irrational number. - T. D. Noe, Jan 10 2007

Examples

			a(1)=0 because 3^(1+1)=9 (one digit) 3^1=3 (one digit) and the difference is 0
a(4)=1 because 3^(4+1)=243 (three digits) 3^(4)=81 (two digits) and the difference is 1
		

Programs

Maple

P:=proc(n) local i,j,k,w,old; k:=3; for i from 1 by 1 to n do j:=k^i; w:=0; while j>0 do w:=w+1; j:=trunc(j/10); od; if i>1 then print(w-old); old:=w; else old:=w; fi; od; end: P(1000);

Mathematica

Differences[IntegerLength[3^Range[0,110]]] (* Harvey P. Dale, Jan 28 2015 *)

Formula

a(n)=Number_of_digits{3^(n+1)}-Number_of digits{3^(n)} with n>=0.