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

Author

Jeff Burch

Keywords

• hard
• nonn
• base

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

Examples

			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)
		

Links

• Index entries for sequences related to factorial numbers

Crossrefs

Cf. A000142.

Programs

Mathematica

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

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