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

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

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