%I
%S 1,2,4,5,8,10,16,20,25,32,40,50,64,80,100,125,128,160,200,250,256,320,
%T 400,500,512,625,640,800,1000,1024,1250,1280,1600,2000,2048,2500,2560,
%U 3125,3200,4000,4096,5000,5120,6250,6400,8000,8192,10000
%N Numbers of the form 2^i*5^j.
%C These are the natural numbers whose reciprocals are terminating decimals. - David Wasserman (wasserma(AT)spawar.navy.mil), Feb 26 2002
%C A132726(a(n),k)=0 for k<=a(n); A051626(a(n))=0; A132740(a(n))=1; A132741(a(n))=a(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 27 2007
%C Where record values greater than 1 occur in A165706: A165707(n)=A165706(a(n)). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 26 2009]
%C Also numbers that are divisible by neither 10k-7, 10k-3, 10k-1 nor 10k+1, for all k > 0. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 26 2010]
%C A204455(5*a(n)) = 5, and only for these numbers. - From Wolfdieter Lang, Feb 04 2012
%H R. Zumkeller, <a href="/A003592/b003592.txt">Table of n, a(n) for n = 1..1000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RegularNumber.html">Regular Number</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DecimalExpansion.html">Decimal Expansion</a>
%t fQ[n_] := PowerMod[10, n, n] == 0; Select[ Range@ 10000, fQ] (* Robert G. Wilson v, Jan 12 2012 *)
%t fQ[n_] := Union[ MemberQ[{1, 3, 7, 9}, # ] & /@ Union@ Mod[ Rest@ Divisors@ n, 10]] == {False}; fQ[1] = True; Select[ Range@ 10000, fQ] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 26 2010]
%t mx = 14; Sort@ Flatten@ Table[2^i*5^j, {i, 0, mx}, {j, 0, Log[5, 2^(mx - i)]}] (* Or *)
%t Union@ Flatten@ NestList[{2#, 4#, 5#} &, 1, 7] (* Robert G. Wilson v, Apr 16 2011 *)
%o (PARI) list(lim)=my(v=List(),N);for(n=0,log(lim)\log(5),N=5^n;while(N<=lim,listput(v,N);N<<=1));vecsort(Vec(v)) \\ Charles R Greathouse IV, Jun 28 2011
%K nonn
%O 1,2
%A N. J. A. Sloane (njas(AT)research.att.com).
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