OFFSET
0,5
COMMENTS
The positive integers which are in the complement to this sequence are: 25, 34, 41, 46, 51, 56, 61, 65, 69, 73, 77, 80, 84, 88, 91, 94, 98, 101, ... because there is no Bell number with 25 digits (B(30) = 846749014511809332450147 has 24 digits, B(31) = 10293358946226376485095653 has 26 digits).
Since a(n) >> n log n, there are infinitely many numbers (indeed, almost all positive integers) in the complement of this sequence. [Charles R Greathouse IV, Aug 10 2011]
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
John Sokol, The First 1000 Bell Numbers.
FORMULA
a(n) = ceiling(log_10 A000110(n)).
a(n) ~ nk log n with k = 1/log 10. More specifically, a(n) = (n log n + n log log n - n + n/W(n) + log n - 0.5 log W(n) - 1)/log 10 + o(1), where W is Lambert's W function W(x)*exp(W(x)) = x. [Charles R Greathouse IV, Aug 11 2011]
EXAMPLE
a(0) = 1 because Bell(0) = 1, which has one digit.
a(1) = 1 because Bell(1) = 1, which has one digit.
a(2) = 1 because Bell(2) = 2, which has one digit.
a(3) = 1 because Bell(3) = 5, which has one digit.
a(4) = 2 because Bell(4) = 15, which has two digits.
MAPLE
seq(length(bell(n)), n = 0 .. 73); # Zerinvary Lajos, Aug 07 2007
PROG
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Jonathan Vos Post, Jan 25 2006
STATUS
approved