A125144 Increments in the number of decimal digits of 4^n.

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

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Jan 11 2007

Keywords

• easy
• nonn
• base

Comments

This sequence is not periodic because log(4)/log(10) is an irrational number. - T. D. Noe, Jan 25 2007

Examples

			a(1)=1 because 4^(1+1)=16 (two digits) 4^1=4 (one digit) and the difference is 1.
a(2)=0 because 4^(2+1)=64 (two digits) 4^(2)=16 (two digits) and the difference is 0.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A125117, A125122.

First differences of A210434.

Programs

Maple

P:=proc(n) local i,j,k,w,old; k:=4; 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);
# alternative:
H:= [seq(ilog10(4^i),i=1..1001)]:
H[2..-1]-H[1..-2]; # Robert Israel, Jul 12 2018

Mathematica

Differences[IntegerLength[4^Range[100]]] (* Paolo Xausa, Jun 08 2024 *)

PARI

a(n) = #digits(4^(n+1)) - #digits(4^n); \\ Michel Marcus, Jul 12 2018

Formula

a(n)=Number_of_digits{4^(n+1)}-Number_of digits{4^(n)} with n>=0 and where "Number_of digits" is a hypothetical function giving the number of digits of the argument.

Extensions

Offset corrected by Robert Israel, Jul 11 2018