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A249829 Numbers n > 1 such that the fractional part of log_10(n!) is less than at any smaller n > 1. 2
2, 5, 22, 27, 35, 95, 104, 197, 5935, 7399, 8998, 11671, 43628, 165535, 258335, 549545, 1542194, 2159448, 3121515, 5814278, 9242360, 21603225, 28563732, 40700787, 252544447, 5042264463, 11012237562, 31774693500, 203839526676, 291409419928, 421559495894 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..31.

EXAMPLE

01: log_10(2!)            =             0.301029995663981+

02: log_10(5!)            =             2.079181246047624+

03: log_10(22!)           =            21.050766592433840+

04: log_10(27!)           =            28.036982790964881+

05: log_10(35!)           =            40.014232648350316+

06: log_10(95!)           =           148.014099417119930+

07: log_10(104!)          =           166.012795764264301+

08: log_10(197!)          =           368.000340377705033+

09: log_10(5935!)         =         19820.000049027723957+

10: log_10(7399!)         =         25417.000038890177487+

11: log_10(8998!)         =         31674.000026273546156+

12: log_10(11671!)        =         42401.000022770999784+

13: log_10(43628!)        =        183479.000020074434223+

14: log_10(165535!)       =        792021.000004677597983+

15: log_10(258335!)       =       1285966.000004657640797+

16: log_10(549545!)       =       2915729.000001700437755+

17: log_10(1542194!)      =       8873548.000001330888624+

18: log_10(2159448!)      =      12740851.000000524918472+

19: log_10(3121515!)      =      18916606.000000301890432+

20: log_10(5814278!)      =      36805554.000000047404977+

21: log_10(9242360!)      =      60366371.000000019402831+

22: log_10(21603225!)     =     149067098.000000015088131+

23: log_10(28563732!)     =     200560833.000000014728648+

24: log_10(40700787!)     =     292040700.000000011129474+

25: log_10(252544447!)    =    2012285104.000000000412667+

26: log_10(5042264463!)   =   46733376736.000000000051832+

27: log_10(11012237562!)  =  105800965362.000000000047200+

28: log_10(31774693500!)  =  319900842599.000000000026403+

29: log_10(203839526676!) = 2216753613325.000000000006671+

30: log_10(291409419928!) = 3214306836834.000000000006605+

31: log_10(421559495894!) = 4717488684964.000000000000681+

PROG

(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

CROSSREFS

Cf. A177901, A250022.

Sequence in context: A298762 A025559 A072961 * A042557 A137097 A024686

Adjacent sequences:  A249826 A249827 A249828 * A249830 A249831 A249832

KEYWORD

nonn

AUTHOR

Jon E. Schoenfield, Nov 10 2014

STATUS

approved

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Last modified September 19 16:01 EDT 2020. Contains 337178 sequences. (Running on oeis4.)