A109336 "Que sera, sera" sequence: self-describing sequence where a(n) gives the number of n+1's which will be concatenated to form a(n+1); starting with a(1) = 1.

1, 2, 33, 444444444444444444444444444444444

Offset: 1

Author

Alexandre Wajnberg, Aug 23 2005

Keywords

• base
• nonn

Examples

			a(1) says: there will be one 2 in a(2).
a(2)=2 because a(1) said so; and a(2)=2 says: there will be two 3's in a(3).
a(3)=33 because a(2) said so; and also a(3) says: there will be thirty three 4's in a(4).
Therefore a(4)= 444444444444444444444444444444444 (33 times the digit 4).
And a(5)= 555555555555555...555 (with 444444444444444444444444444444444 5's).
		

Crossrefs

Cf. A001462, A001463, A103320, A102357, A076782.

Formula

a(1) = 1. For n > 1, let k = floor(1+log_10(n)); then a(n) = n*(10^(k*a(n-1))-1)/(10^k-1).

Extensions

Formula corrected to handle n>9 also by Rick L. Shepherd, Mar 22 2009