%I A007496 M0497
%S A007496 0,1,2,3,4,5,6,7,9,18,33
%N A007496 Numbers n such that the decimal expansions of 2^n and 5^n contain no 
               0's (probably 33 is last term).
%C A007496 Intersection of A007377 and A008839. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Jul 27 2004
%C A007496 Comments from Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 20 2005 
               (Start): Equivalently, numbers n such that 10^n is the product of 
               two integers without any zero digits.
%C A007496 The first number must be some power of 2, the second the same power of 
               5. Such a pair is the only positive solution because neither factor 
               could have both a 2 and a 5 in its prime factorization, or else it 
               would be a multiple of 10 and would thus have a 0 as its last digit, 
               which is ruled out. "We may wonder what powers of 10 are products 
               of two integers without any zero digits. For large numbers, this 
               is very unlikely because there will normally be 10% of zeros among 
               many random digits... In fact, there seems to be only 11 possibilities... 
               The probability is roughly (0.9)^n that the n-th power of 10 would 
               yield a solution. So the expected number of solutions above the n-th 
               power of 10 is someting like 10*(0.9)^n. Since we've actually checked 
               that there's no other solution below n = 1500, we can be very confident 
               that we've not missed anything..."
%C A007496 10^0 = 1 * 1
%C A007496 10^1 = 2 * 5
%C A007496 10^2 = 4 * 25
%C A007496 10^3 = 8 * 125
%C A007496 10^4 = 16 * 625
%C A007496 10^5 = 32 * 3125
%C A007496 10^6 = 64 * 15625
%C A007496 10^7 = 128 * 78125
%C A007496 10^9 = 512 * 1953125
%C A007496 10^18 = 262144 * 3814697265625
%C A007496 10^33 = 8589934592 * 116415321826934814453125 (End)
%D A007496 Leroy C. Dalton & Henry D. Snyder, Topics for Mathematics Clubs, pp. 
               68-69, NCTM Reston VA 1983.
%D A007496 J. S. Madachy, Madachy's Mathematical Recreation, "#2. Number Toughies", 
               pp. 126-8, Dover NY 1979.
%D A007496 C. S. Ogilvy and J. T. Anderson, Excursions in Number Theory. Oxford 
               Univ. Press, 1966, p. 89.
%D A007496 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007496 G. P. Michon, <a href="http://home.att.net/~numericana/answer/numbers.htm#nozero">
               What two integers without zero digits have a product of 1000000000?</
               a>
%H A007496 W. Schneider, <a href="http://www.wschnei.de/digit-related-numbers/nozeros.html">
               NoZeros</a> [Broken link]
%H A007496 W. Schneider, <a href="a007496.html">NoZeros</a> [Cached copy]
%Y A007496 Sequence in context: A048319 A037405 A048333 this_sequence A082274 A029804 
               A084690
%Y A007496 Adjacent sequences: A007493 A007494 A007495 this_sequence A007497 A007498 
               A007499
%K A007496 fini,nonn,full,base
%O A007496 1,3
%A A007496 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
%E A007496 Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 24 2009 at 
               the suggestion of M. F. Hasler