A125144 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

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

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.

EXAMPLE

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.

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 *)

PROG

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

CROSSREFS

Cf. A125117, A125122.

First differences of A210434.

Sequence in context: A128174 A096055 A260456 * A115198 A005614 A341753

Adjacent sequences: A125141 A125142 A125143 * A125145 A125146 A125147