cp's OEIS Frontend

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).

%I A181754 #7 Mar 30 2012 18:40:13
%S A181754 1,2,6,21,601,21001,60100001,2100100000001,601000010000000000001,
%T A181754 2100100000001000000000000000000001,
%U A181754 6010000100000000000010000000000000000000000000000000001
%N 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).
%C A181754 The calculations for the first few values of the sequence are
%C A181754 ... a(3) = 12/2 = 6
%C A181754 ... a(4) = 126/6 = 21
%C A181754 ... a(5) = 12621/21 = 601
%C A181754 ... a(6) = 12621601/601 = 21001.
%C A181754 Similar sequences may be formed by
%C A181754 1) starting with different initial values. See A181755 and A181756.
%C A181754 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 A181754 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 A181754 DEFINITION
%F A181754 a(1) = 1, a(2) = 2, and for n >= 3
%F A181754 (1)... a(n) = concatenate(a(1),a(2),...,a(n-1))/a(n-1).
%F A181754 RECURRENCE RELATION
%F A181754 For n >= 2
%F A181754 (2)... a(n+2) = 10^F(n)*a(n)+1,
%F A181754 where F(n) = A000045(n) are the Fibonacci numbers.
%F A181754 For n >= 2, a(n) has F(n-1) digits.
%p A181754 #A181754
%p A181754 M:=11:
%p A181754 a:=array(1..M):s:=array(1..M):
%p A181754 a[1]:=1:a[2]:=2:
%p A181754 s[1]:=convert(a[1],string):
%p A181754 s[2]:=cat(s[1],convert(a[2],string)):
%p A181754 for n from 3 to M do
%p A181754 a[n] := parse(s[n-1])/a[n-1];
%p A181754 s[n]:= cat(s[n-1],convert(a[n],string));
%p A181754 end do:
%p A181754 seq(a[n],n = 1..M);
%Y A181754 Cf. A000045, A181755, A181756, A181864, A181865, A181866, A181867, A181868, A181869, A181870
%K A181754 easy,nonn,base
%O A181754 1,2
%A A181754 _Peter Bala_, Nov 09 2010