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A105565
a(n) = if (exactly 5 Fibonacci numbers exist with exactly n digits) then 1, otherwise 0.
4
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
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
KEYWORD
nonn,base
AUTHOR
Reinhard Zumkeller, Apr 14 2005
STATUS
approved