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A033147 Numbers k such that the decimal expansion of k! begins with k. 2
1, 2, 198, 217, 5936, 7400, 8999, 11672, 5814279, 9242361, 10430012, 21603226, 28563733, 252544448, 5042264464, 5795685640, 421559495895 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
hard,nonn,base
AUTHOR
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

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)