A181754 - OEIS

%I #7 Mar 30 2012 18:40:13

%S 1,2,6,21,601,21001,60100001,2100100000001,601000010000000000001,

%T 2100100000001000000000000000000001,

%U 6010000100000000000010000000000000000000000000000000001

%N 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).

%C The calculations for the first few values of the sequence are

%C ... a(3) = 12/2 = 6

%C ... a(4) = 126/6 = 21

%C ... a(5) = 12621/21 = 601

%C ... a(6) = 12621601/601 = 21001.

%C Similar sequences may be formed by

%C 1) starting with different initial values. See A181755 and A181756.

%C 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.

%C 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.

%F DEFINITION

%F a(1) = 1, a(2) = 2, and for n >= 3

%F (1)... a(n) = concatenate(a(1),a(2),...,a(n-1))/a(n-1).

%F RECURRENCE RELATION

%F For n >= 2

%F (2)... a(n+2) = 10^F(n)*a(n)+1,

%F where F(n) = A000045(n) are the Fibonacci numbers.

%F For n >= 2, a(n) has F(n-1) digits.

%p #A181754

%p M:=11:

%p a:=array(1..M):s:=array(1..M):

%p a[1]:=1:a[2]:=2:

%p s[1]:=convert(a[1],string):

%p s[2]:=cat(s[1],convert(a[2],string)):

%p for n from 3 to M do

%p a[n] := parse(s[n-1])/a[n-1];

%p s[n]:= cat(s[n-1],convert(a[n],string));

%p end do:

%p seq(a[n],n = 1..M);

%Y Cf. A000045, A181755, A181756, A181864, A181865, A181866, A181867, A181868, A181869, A181870

%K easy,nonn,base

%O 1,2

%A _Peter Bala_, Nov 09 2010