A085769 - OEIS

%I #10 Dec 15 2017 17:36:28

%S 0,0,0,0,0,0,0,1,0,1,1,2,2,1,1,1,1,0,1,2,2,2,3,2,1,2,2,2,3,1,1,2,0,3,

%T 3,2,2,4,3,5,2,3,4,5,8,5,5,6,4,4,4,8,9,5,7,4,3,1,5,6,8,8,9,10,7,7,5,8,

%U 11,11,7,8,5,4,4,6,5,6,8,10,7,6,7,4,2,4,9,9,7,9,9,8,10,10,5,5,8,11,14,18

%N Total number of zeros in the decimal expansions of 2^n and 5^n.

%C 10^33 is believed to be the largest power of 10 that can be expressed as the product of 2 numbers which contain no zero digits.

%D C. Stanley Ogilvy and John T. Anderson, Excursions in Number Theory. Dover. New York: 1988. Page 89.

%D C. Pickover, Wonders of Numbers, Oxford University Press, NY, 2001, pp. 201-202, 353.

%H C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," <a href="http://www.zentralblatt-math.org/zmath/en/search/?q=an:0983.00008&amp;format=complete">Zentralblatt review</a>

%e a(58)=1 because 10^58 = 288230376151711744 * 34694469519536141888238489627838134765625

%e and the latter two numbers contain only one zero between them.

%K nonn,base

%O 1,12

%A _Jason Earls_, Jul 22 2003