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%I #38 Feb 26 2022 16:32:18
%S 2,5,22,27,35,95,104,197,5935,7399,8998,11671,43628,165535,258335,
%T 549545,1542194,2159448,3121515,5814278,9242360,21603225,28563732,
%U 40700787,252544447,5042264463,11012237562,31774693500,203839526676,291409419928,421559495894
%N Numbers m > 1 such that the fractional part of log_10(m!) is less than at any smaller m > 1.
%C This sequence is similar to A177901 (Numbers n > 1 such that s(n) = Sum_{k=2..n} log_10(k) is closer to an integer than at any smaller n) except that the values of s(n) are approaching integers strictly from above.
%e 01: log_10(2!) = 0.301029995663981+
%e 02: log_10(5!) = 2.079181246047624+
%e 03: log_10(22!) = 21.050766592433840+
%e 04: log_10(27!) = 28.036982790964881+
%e 05: log_10(35!) = 40.014232648350316+
%e 06: log_10(95!) = 148.014099417119930+
%e 07: log_10(104!) = 166.012795764264301+
%e 08: log_10(197!) = 368.000340377705033+
%e 09: log_10(5935!) = 19820.000049027723957+
%e 10: log_10(7399!) = 25417.000038890177487+
%e 11: log_10(8998!) = 31674.000026273546156+
%e 12: log_10(11671!) = 42401.000022770999784+
%e 13: log_10(43628!) = 183479.000020074434223+
%e 14: log_10(165535!) = 792021.000004677597983+
%e 15: log_10(258335!) = 1285966.000004657640797+
%e 16: log_10(549545!) = 2915729.000001700437755+
%e 17: log_10(1542194!) = 8873548.000001330888624+
%e 18: log_10(2159448!) = 12740851.000000524918472+
%e 19: log_10(3121515!) = 18916606.000000301890432+
%e 20: log_10(5814278!) = 36805554.000000047404977+
%e 21: log_10(9242360!) = 60366371.000000019402831+
%e 22: log_10(21603225!) = 149067098.000000015088131+
%e 23: log_10(28563732!) = 200560833.000000014728648+
%e 24: log_10(40700787!) = 292040700.000000011129474+
%e 25: log_10(252544447!) = 2012285104.000000000412667+
%e 26: log_10(5042264463!) = 46733376736.000000000051832+
%e 27: log_10(11012237562!) = 105800965362.000000000047200+
%e 28: log_10(31774693500!) = 319900842599.000000000026403+
%e 29: log_10(203839526676!) = 2216753613325.000000000006671+
%e 30: log_10(291409419928!) = 3214306836834.000000000006605+
%e 31: log_10(421559495894!) = 4717488684964.000000000000681+
%o (PARI) n=2;f=1;while(n,if((F=frac(lngamma(n+1)/log(10)))<f,f=F;print1(n,", "));n++) \\ _Derek Orr_, Nov 13 2014
%Y Cf. A177901, A250022.
%K nonn
%O 1,1
%A _Jon E. Schoenfield_, Nov 10 2014
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