A033147 Numbers k such that the decimal expansion of k! begins with k.

1, 2, 198, 217, 5936, 7400, 8999, 11672, 5814279, 9242361, 10430012, 21603226, 28563733, 252544448, 5042264464, 5795685640, 421559495895

Offset

1,2

Comments

The inclusion of the deleted term k=171489648 seems likely to have resulted from a precision problem: computing as an intermediate result x = log_10(k!) = 1337609557.23423787495... and storing that result rounded to its nearest IEEE 754 double-precision binary floating-point number D = 5610341116345793 / 2^22 would result in floor(10^(D-1337609549)) = 171489648 = k, whereas floor(10^(x-1337609549)) = 171489634. - Jon E. Schoenfield, Nov 07 2014

Links

Table of n, a(n) for n=1..17.

Index entries for sequences related to factorial numbers

Example

From Jon E. Schoenfield, Nov 07 2014: (Start)
         198! =          198.155...*10^368
         217! =          217.443...*10^412
        5936! =         5936.670...*10^19820
        7400! =         7400.662...*10^25417
        8999! =         8999.544...*10^31674
       11672! =        11672.612...*10^42401
     5814279! =      5814279.634...*10^36805554
     9242361! =      9242361.412...*10^60366371
    10430012! =     10430012.795...*10^68671095
    21603226! =     21603226.750...*10^149067098
    28563733! =     28563733.968...*10^200560833
   252544448! =    252544448.239...*10^2012285104
  5042264464! =   5042264464.601...*10^46733376736
  5795685640! =   5795685640.984...*10^54066852117
421559495895! = 421559495895.661...*10^4717488684964
(End)

Mathematica

Do[ If[ RealDigits[ n ][ [ 1 ] ] == Take[ RealDigits[ n! ][ [ 1 ] ], RealDigits[ n ][ [ 2 ] ] ], Print[ n ] ], {n, 1, 10^5} ]

Crossrefs

Cf. A000142.

Sequence in context: A174367 A262650 A123100 * A213162 A124339 A089772

Adjacent sequences: A033144 A033145 A033146 * A033148 A033149 A033150

Keyword

hard,nonn,base

Author

Jeff Burch

Extensions

More terms from David W. Wilson

Incorrect term 171489648 deleted and terms a(13)-a(17) added by Jon E. Schoenfield, Nov 07 2014

Status

approved