A224782 Length of longest run of consecutive zeros in decimal representation of 2^n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1

Offset: 0

Author

Reinhard Zumkeller, Apr 30 2013

Keywords

• nonn
• base

Comments

a(n) <= A027870(n);

a(A007377(n)) = 0;

a(A006889(n)) = n and a(m) <> n for m < A006889(n).

References

• Julian Havil, Impossible?: Surprising Solutions to Counterintuitive Conundrums, Princeton University Press 2008, chapter 15, p. 176ff

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Programs

Haskell

import Data.List (group)
a224782 n = a224782_list !! n
a224782_list = map (foldl h 0 . group . show) a000079_list where
   h x zs@(z:_) = if z == '0' then max x $ length zs else x