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A006488 n! has a square number of digits.
(Formerly M0830)
2

%I M0830

%S 0,1,2,3,7,12,18,32,59,81,105,132,228,265,284,304,367,389,435,483,508,

%T 697,726,944,1011,1045,1080,1115,1187,1454,1494,1617,1659,1788,1921,

%U 2012,2105,2200,2248,2395,2445,2861,2915,3192,3480,3539,3902,3964,4476

%N n! has a square number of digits.

%D M. Gardner, Mathematical Magic Show. Random House, NY, 1978, p. 55.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

%t LogBase10Stirling[n_] := Floor[Log[10, 2 Pi n]/2 + n*Log[10, n/E] + Log[10, 1 + 1/(12n) + 1/(288n^2) - 139/(51840n^3) - 571/(2488320n^4) + 163879/(209018880n^5)]]; Select[ Range[ 4500], IntegerQ[ Sqrt[ (LogBase10Stirling[ # ] + 1)]] & ]

%Y Cf. A000142, A056851.

%K nonn,base

%O 0,3

%A _N. J. A. Sloane_, _Robert G. Wilson v_

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Last modified April 19 05:22 EDT 2014. Contains 240738 sequences.