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A181756
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a(1) = 1, a(2) = 10. For n >= 3, a(n) is found by concatenating the first n-1 terms of the sequence and then dividing the resulting number by a(n-1).
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10
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1, 10, 11, 1001, 110001, 1001000001, 1100010000000001, 10010000010000000000000001, 110001000000000100000000000000000000000001, 10010000010000000000000001000000000000000000000000000000000000000001
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OFFSET
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1,2
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COMMENTS
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The calculations for the first few values of the sequence are
... a(3) = 110/10 = 11
... a(4) = 11011/11 = 1001
... a(5) = 110111001/1001 = 110001.
The above calculations are in base 10, but we get exactly the same results when working in an arbitrary base b. For example, with starting values a(1) = 1, a(2) = b (= 10 in base b), we get
... a(3) = (b^2+b)/b = b+1 which equals 11 in base b,
... a(4) = (b^4+b^3+b+1))/(b+1) = b^3+1 = 1001 in base b,
and so on.
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LINKS
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FORMULA
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DEFINITION
a(1) = 1, a(2) = 10, and for n >= 3
(1)... a(n) = concatenate(a(1),a(2),...,a(n-1))/a(n-1).
RECURRENCE RELATION
For n >= 2
(2)... a(n+2) = 100^F(n)*a(n)+1,
where F(n) = A000045(n) are the Fibonacci numbers.
For n >= 2, a(n) has 2*F(n-1) digits.
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MAPLE
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M:=10:
a:=array(1..M):s:=array(1..M):
a[1]:=1:a[2]:=10:
s[1]:=convert(a[1], string):
s[2]:=cat(s[1], convert(a[2], string)):
for n from 3 to M do
a[n] := parse(s[n-1])/a[n-1];
s[n]:= cat(s[n-1], convert(a[n], string));
end do:
seq(a[n], n = 1..M);
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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STATUS
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approved
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