Search: id:A006488
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%I A006488 M0830
%S A006488 0,1,2,3,7,12,18,32,59,81,105,132,228,265,284,304,367,389,435,483,508,
%T A006488 697,726,944,1011,1045,1080,1115,1187,1454,1494,1617,1659,1788,1921,
%U A006488 2012,2105,2200,2248,2395,2445,2861,2915,3192,3480,3539,3902,3964,4476
%N A006488 n! has a square number of digits.
%D A006488 M. Gardner, Mathematical Magic Show. Random House, NY, 1978, p. 55.
%D A006488 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006488 <a href="Sindx_Fa.html#factorial">Index entries for sequences related 
               to factorial numbers</a>
%t A006488 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 A006488 Cf. A000142, A056851.
%Y A006488 Sequence in context: A066733 A049623 A061577 this_sequence A121430 A023606 
               A157605
%Y A006488 Adjacent sequences: A006485 A006486 A006487 this_sequence A006489 A006490 
               A006491
%K A006488 nonn,base
%O A006488 0,3
%A A006488 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)

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