cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A249829 Numbers m > 1 such that the fractional part of log_10(m!) is less than at any smaller m > 1.

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%I A249829 #38 Feb 26 2022 16:32:18
%S A249829 2,5,22,27,35,95,104,197,5935,7399,8998,11671,43628,165535,258335,
%T A249829 549545,1542194,2159448,3121515,5814278,9242360,21603225,28563732,
%U A249829 40700787,252544447,5042264463,11012237562,31774693500,203839526676,291409419928,421559495894
%N A249829 Numbers m > 1 such that the fractional part of log_10(m!) is less than at any smaller m > 1.
%C A249829 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 A249829 01: log_10(2!)            =             0.301029995663981+
%e A249829 02: log_10(5!)            =             2.079181246047624+
%e A249829 03: log_10(22!)           =            21.050766592433840+
%e A249829 04: log_10(27!)           =            28.036982790964881+
%e A249829 05: log_10(35!)           =            40.014232648350316+
%e A249829 06: log_10(95!)           =           148.014099417119930+
%e A249829 07: log_10(104!)          =           166.012795764264301+
%e A249829 08: log_10(197!)          =           368.000340377705033+
%e A249829 09: log_10(5935!)         =         19820.000049027723957+
%e A249829 10: log_10(7399!)         =         25417.000038890177487+
%e A249829 11: log_10(8998!)         =         31674.000026273546156+
%e A249829 12: log_10(11671!)        =         42401.000022770999784+
%e A249829 13: log_10(43628!)        =        183479.000020074434223+
%e A249829 14: log_10(165535!)       =        792021.000004677597983+
%e A249829 15: log_10(258335!)       =       1285966.000004657640797+
%e A249829 16: log_10(549545!)       =       2915729.000001700437755+
%e A249829 17: log_10(1542194!)      =       8873548.000001330888624+
%e A249829 18: log_10(2159448!)      =      12740851.000000524918472+
%e A249829 19: log_10(3121515!)      =      18916606.000000301890432+
%e A249829 20: log_10(5814278!)      =      36805554.000000047404977+
%e A249829 21: log_10(9242360!)      =      60366371.000000019402831+
%e A249829 22: log_10(21603225!)     =     149067098.000000015088131+
%e A249829 23: log_10(28563732!)     =     200560833.000000014728648+
%e A249829 24: log_10(40700787!)     =     292040700.000000011129474+
%e A249829 25: log_10(252544447!)    =    2012285104.000000000412667+
%e A249829 26: log_10(5042264463!)   =   46733376736.000000000051832+
%e A249829 27: log_10(11012237562!)  =  105800965362.000000000047200+
%e A249829 28: log_10(31774693500!)  =  319900842599.000000000026403+
%e A249829 29: log_10(203839526676!) = 2216753613325.000000000006671+
%e A249829 30: log_10(291409419928!) = 3214306836834.000000000006605+
%e A249829 31: log_10(421559495894!) = 4717488684964.000000000000681+
%o A249829 (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 A249829 Cf. A177901, A250022.
%K A249829 nonn
%O A249829 1,1
%A A249829 _Jon E. Schoenfield_, Nov 10 2014