A105565 a(n) = if (exactly 5 Fibonacci numbers exist with exactly n digits) then 1, otherwise 0.

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

Offset

1,1

Comments

The sequence is almost periodic, see also A105566;

a(n) = 1 - A105563(n) for n > 1.

Links

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

Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

Jürgen Spilker, Die Ziffern der Fibonacci-Zahlen, Elemente der Mathematik 58 (Birkhäuser 2003).

Eric Weisstein's World of Mathematics, Fibonacci Number

Eric Weisstein's World of Mathematics, Almost Periodic Function

Maple

n:= 1: count:= 2: a:= 0: b:= 1:
for m from 2 while n < 101 do
  c:= b; b:= a+b; a:= c;
  s:= ilog10(b)+1;
  if s = n then count:= count+1
  else
    if count = 5 then A[n]:= 1 else A[n]:= 0 fi;
    count:= 1; n:= s
  fi
od:
seq(A[i], i=1..100); # Robert Israel, Dec 17 2018

Crossrefs

Cf. A050815, A060384, A000045.

Sequence in context: A144610 A188068 A181632 * A332814 A353788 A348737

Adjacent sequences: A105562 A105563 A105564 * A105566 A105567 A105568

Keyword

nonn,base

Author

Reinhard Zumkeller, Apr 14 2005

Status

approved