A250022 Numbers m > 1 such that the fractional part of log_10(m!) is greater than at any smaller m > 1.

2, 3, 6, 14, 29, 79, 96, 261, 8765, 17411, 108965, 583104, 833851, 1692693, 2064173, 4146167, 4594140, 12861320, 46464264, 54336595, 54528830, 364469152, 1175842443, 1430841730, 9167724225, 40752166709, 46787073630, 128693978358, 129532358256, 6194978274594

Offset: 1

Author

Jon E. Schoenfield, Nov 10 2014

Keywords

• nonn

Comments

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.

Examples

			01: log_10(2!)            =             0.301029995663981+
02: log_10(3!)            =             0.778151250383643+
03: log_10(6!)            =             2.857332496431268+
04: log_10(14!)           =            10.940408352067718+
05: log_10(29!)           =            30.946538820206057+
06: log_10(79!)           =           116.951637735507649+
07: log_10(96!)           =           149.996370650159498+
08: log_10(261!)          =           518.999861489950633+
09: log_10(8765!)         =         30753.999918708768634+
10: log_10(17411!)        =         66277.999990331137038+
11: log_10(108965!)       =        501567.999995101004009+
12: log_10(583104!)       =       3108793.999995955509958+
13: log_10(833851!)       =       4575171.999998004577195+
14: log_10(1692693!)      =       9807946.999998415147545+
15: log_10(2064173!)      =      12138272.999999698549856+
16: log_10(4146167!)      =      25637214.999999864901639+
17: log_10(4594140!)      =      28611892.999999950670122+
18: log_10(12861320!)     =      85849199.999999970372496+
19: log_10(46464264!)     =     336067874.999999977837282+
20: log_10(54336595!)     =     396700504.999999987676435+
21: log_10(54528830!)     =     398187607.999999992752989+
22: log_10(364469152!)    =    2962174305.999999997663445+
23: log_10(1175842443!)   =   10154639602.999999998805009+
24: log_10(1430841730!)   =   12478795857.999999999673704+
25: log_10(9167724225!)   =   87349774425.999999999908570+
26: log_10(40752166709!)  =  414688189184.999999999986848+
27: log_10(46787073630!)  =  478904597405.999999999986917+
28: log_10(128693978358!) = 1373842161327.999999999991789+
29: log_10(129532358256!) = 1383157375034.999999999999183+
30: log_10(6194978274594!)=76555963692202.999999999999259+
		

Crossrefs

Cf. A177901, A249829.