%I A088995
%S A088995 5,98,1068,1068,127185,2728361,15917834
%N A088995 Least k>0 such that the first n digits of 2^k and 5^k are identical.
%C A088995 The number of matching first digits of 2^n and 5^n increases with n and 
               forms the sequence 3,1,6,2,2,7,7,6,6,... which approaches Sqrt(10).
%H A088995 T. Sillke, <a href="http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/
               powers-2-5">Powers of 2 and 5 Puzzle</a>
%e A088995 a(2) = 98: 2^98 = 316912650057057350374175801344 and 5^98 = 3155443620884047221646914261131144918692825740436\
               09201908111572265625.
%t A088995 L2 = N[ Log[ 10, 2 ], 50 ]; L5 = N[ Log[ 10, 5 ], 50 ]; k = 1; Do[ While[ 
               Take[ RealDigits[ 10^FractionalPart[ L2*k ] ][[ 1 ] ], n ] != Take[ 
               RealDigits[ 10^FractionalPart[ L5*k ] ][[ 1 ] ], n ], k++ ]; Print[ 
               k ], {n, 1, 10} ]
%t A088995 L2 = N[ Log[ 10, 2 ], 50 ]; L5 = N[ Log[ 10, 5 ], 50 ]; k = 1; Do[ While[ 
               Take[ RealDigits[ 10^FractionalPart[ L2*k ]][[ 1 ]], n ] != Take[ 
               RealDigits[ 10^FractionalPart[ L5*k ]][[ 1 ]], n ], k++ ]; Print[ 
               k ], {n, 1, 7} ]
%Y A088995 Cf. A088935.
%Y A088995 Cf. A010467.
%Y A088995 Sequence in context: A117341 A062538 A053980 this_sequence A093749 A147539 
               A156276
%Y A088995 Adjacent sequences: A088992 A088993 A088994 this_sequence A088996 A088997 
               A088998
%K A088995 base,nonn
%O A088995 1,1
%A A088995 Lekraj Beedassy (blekraj(AT)yahoo.com), Dec 01 2003
%E A088995 Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 02 2003