cp's OEIS Frontend

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

%I A033147 #27 Aug 07 2021 01:27:40
%S A033147 1,2,198,217,5936,7400,8999,11672,5814279,9242361,10430012,21603226,
%T A033147 28563733,252544448,5042264464,5795685640,421559495895
%N A033147 Numbers k such that the decimal expansion of k! begins with k.
%C A033147 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
%H A033147 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%e A033147 From _Jon E. Schoenfield_, Nov 07 2014: (Start)
%e A033147          198! =          198.155...*10^368
%e A033147          217! =          217.443...*10^412
%e A033147         5936! =         5936.670...*10^19820
%e A033147         7400! =         7400.662...*10^25417
%e A033147         8999! =         8999.544...*10^31674
%e A033147        11672! =        11672.612...*10^42401
%e A033147      5814279! =      5814279.634...*10^36805554
%e A033147      9242361! =      9242361.412...*10^60366371
%e A033147     10430012! =     10430012.795...*10^68671095
%e A033147     21603226! =     21603226.750...*10^149067098
%e A033147     28563733! =     28563733.968...*10^200560833
%e A033147    252544448! =    252544448.239...*10^2012285104
%e A033147   5042264464! =   5042264464.601...*10^46733376736
%e A033147   5795685640! =   5795685640.984...*10^54066852117
%e A033147 421559495895! = 421559495895.661...*10^4717488684964
%e A033147 (End)
%t A033147 Do[ If[ RealDigits[ n ][ [ 1 ] ] == Take[ RealDigits[ n! ][ [ 1 ] ], RealDigits[ n ][ [ 2 ] ] ], Print[ n ] ], {n, 1, 10^5} ]
%Y A033147 Cf. A000142.
%K A033147 hard,nonn,base
%O A033147 1,2
%A A033147 _Jeff Burch_
%E A033147 More terms from _David W. Wilson_
%E A033147 Incorrect term 171489648 deleted and terms a(13)-a(17) added by _Jon E. Schoenfield_, Nov 07 2014