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%I #27 Feb 26 2022 16:30:34
%S 2,3,6,14,29,79,96,261,8765,17411,108965,583104,833851,1692693,
%T 2064173,4146167,4594140,12861320,46464264,54336595,54528830,
%U 364469152,1175842443,1430841730,9167724225,40752166709,46787073630,128693978358,129532358256,6194978274594
%N Numbers m > 1 such that the fractional part of log_10(m!) is greater than at any smaller m > 1.
%C This sequence is similar to A177901 ("Numbers n > 1 such that Sum_{k=2..n} log_10(k) is closer to an integer than at any smaller n") except that the values of the sums are approaching integers strictly from below.
%e 01: log_10(2!) = 0.301029995663981+
%e 02: log_10(3!) = 0.778151250383643+
%e 03: log_10(6!) = 2.857332496431268+
%e 04: log_10(14!) = 10.940408352067718+
%e 05: log_10(29!) = 30.946538820206057+
%e 06: log_10(79!) = 116.951637735507649+
%e 07: log_10(96!) = 149.996370650159498+
%e 08: log_10(261!) = 518.999861489950633+
%e 09: log_10(8765!) = 30753.999918708768634+
%e 10: log_10(17411!) = 66277.999990331137038+
%e 11: log_10(108965!) = 501567.999995101004009+
%e 12: log_10(583104!) = 3108793.999995955509958+
%e 13: log_10(833851!) = 4575171.999998004577195+
%e 14: log_10(1692693!) = 9807946.999998415147545+
%e 15: log_10(2064173!) = 12138272.999999698549856+
%e 16: log_10(4146167!) = 25637214.999999864901639+
%e 17: log_10(4594140!) = 28611892.999999950670122+
%e 18: log_10(12861320!) = 85849199.999999970372496+
%e 19: log_10(46464264!) = 336067874.999999977837282+
%e 20: log_10(54336595!) = 396700504.999999987676435+
%e 21: log_10(54528830!) = 398187607.999999992752989+
%e 22: log_10(364469152!) = 2962174305.999999997663445+
%e 23: log_10(1175842443!) = 10154639602.999999998805009+
%e 24: log_10(1430841730!) = 12478795857.999999999673704+
%e 25: log_10(9167724225!) = 87349774425.999999999908570+
%e 26: log_10(40752166709!) = 414688189184.999999999986848+
%e 27: log_10(46787073630!) = 478904597405.999999999986917+
%e 28: log_10(128693978358!) = 1373842161327.999999999991789+
%e 29: log_10(129532358256!) = 1383157375034.999999999999183+
%e 30: log_10(6194978274594!)=76555963692202.999999999999259+
%Y Cf. A177901, A249829.
%K nonn
%O 1,1
%A _Jon E. Schoenfield_, Nov 10 2014
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