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A181754
a(1) = 1, a(2) = 2. 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).
10
1, 2, 6, 21, 601, 21001, 60100001, 2100100000001, 601000010000000000001, 2100100000001000000000000000000001, 6010000100000000000010000000000000000000000000000000001
OFFSET
1,2
COMMENTS
The calculations for the first few values of the sequence are
... a(3) = 12/2 = 6
... a(4) = 126/6 = 21
... a(5) = 12621/21 = 601
... a(6) = 12621601/601 = 21001.
Similar sequences may be formed by
1) starting with different initial values. See A181755 and A181756.
2) concatenating the k-th powers of the first n-1 terms of the sequence before dividing by a(n-1). See A181864, A181865 and A181866.
3) concatenating the k-th powers of the first n-1 terms of the sequence in reverse order before dividing by a(n-1). See A181867, A181868, A181869 and A181870.
FORMULA
DEFINITION
a(1) = 1, a(2) = 2, 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) = 10^F(n)*a(n)+1,
where F(n) = A000045(n) are the Fibonacci numbers.
For n >= 2, a(n) has F(n-1) digits.
MAPLE
M:=11:
a:=array(1..M):s:=array(1..M):
a[1]:=1:a[2]:=2:
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);
KEYWORD
easy,nonn,base
AUTHOR
Peter Bala, Nov 09 2010
STATUS
approved