

A113865


Number of digits of Bell number A000110(n).


1



1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 70, 71, 72, 74, 75, 76, 78
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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



FORMULA

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



PROG

(Python)
from sympy import bell


CROSSREFS



KEYWORD

base,nonn


AUTHOR



STATUS

approved



