A181868 a(1) = 10, a(2) = 1. For n >= 3, a(n) = concatenate a(n-1), a(n-2), ..., a(1) and then divide the resulting number by a(n-1).

10, 1, 110, 1001, 1000110, 10000001001, 100000000001000110, 10000000000000000010000001001, 10000000000000000000000000000100000000001000110, 1000000000000000000000000000000000000000000000010000000000000000010000001001

Offset: 1

Author

Peter Bala, Nov 28 2010

Keywords

• nonn
• easy

Comments

Compare with A181756.

The calculations for the first few values of the sequence are

... a(3) = 110/1 = 110

... a(4) = 110110/110 = 1001

... a(5) = 1001110110 /1001 = 1000110

... a(6) = 10001101001110110/1000110 = 10000001001.

The above calculations are in base 10, but we get exactly the same results when working in an arbitrary base b with initial values a(1) = 10 (= b in base b), a(2) = 1.

For similarly defined sequences see A181754 through A181756 and A181864 through A181870.

Crossrefs

A000032, A181754 - A181756, A181864 - A181870

Programs

Maple

#A181868
M:=10:
a:=array(1..M):s:=array(1..M):
a[1]:=10:a[2]:=1:
s[1]:=convert(a[1],string):
s[2]:=cat(convert(a[2],string),s[1]):
for n from 3 to M do
a[n] := parse(s[n-1])/a[n-1];
s[n]:= cat(convert(a[n],string),s[n-1]);
end do:
seq(a[n],n = 1..M);

Formula

a(n+2) = a(n) + 10^(A000032(n+1)-1), n>=1.

a(n) has A000032(n-1) digits.