1,1

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).

T. Sillke, Powers of 2 and 5 Puzzle

a(2) = 98: 2^98 = 316912650057057350374175801344 and 5^98 = 315544362088404722164691426113114491869282574043609201908111572265625.

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} ]

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} ]

Cf. A088935.

Cf. A010467.

Sequence in context: A117341 A062538 A053980 this_sequence A093749 A147539 A156276

Adjacent sequences: A088992 A088993 A088994 this_sequence A088996 A088997 A088998

base,nonn

Lekraj Beedassy (blekraj(AT)yahoo.com), Dec 01 2003

Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 02 2003