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.
%I A004790 #20 Jun 22 2021 01:01:17
%S A004790 2,3,8,21,55,149,404,1097,2981,162755,1202605,3269018,8886111,
%T A004790 24154953,178482301,9744803447,26489122130,195729609429,532048240602,
%U A004790 1446257064292,3931334297145,10686474581525,29048849665248,78962960182681,583461742527455,1586013452313431
%N A004790 Numbers k >= 2 such that if 1 < j < k then (fractional part of log k) < (fractional part of log j).
%C A004790 Sequence lists all numbers k > 1 for which the fractional part of log(k) reaches a record low. For n > 1, this can happen only when a(n) = ceiling(e^m) for some positive integer m; see Example section. - _Jon E. Schoenfield_, May 28 2018
%H A004790 Jon E. Schoenfield, <a href="/A004790/b004790.txt">Table of n, a(n) for n = 1..100</a>
%e A004790 From _Jon E. Schoenfield_, May 28 2018: (Start)
%e A004790 k = ceiling(e^m) yields a term for some but not all positive integers m:
%e A004790 .
%e A004790 m | k=ceiling(e^m) | log(k)
%e A004790 ---+---------------------------+--------------------------
%e A004790 1 | 3 = a(2) | 1.0986122886681096913...
%e A004790 2 | 8 = a(3) | 2.0794415416798359282...
%e A004790 3 | 21 = a(4) | 3.0445224377234229965...
%e A004790 4 | 55 = a(5) | 4.0073331852324709186...
%e A004790 5 | 149 = a(6) | 5.0039463059454591409...
%e A004790 6 | 404 = a(7) | 6.0014148779611500697...
%e A004790 7 | 1097 = a(8) | 7.0003344602752302459...
%e A004790 8 | 2981 = a(9) | 8.0000140936780714441...
%e A004790 9 | 8104 | 9.0001130459285193087...
%e A004790 10 | 22027 | 10.0000242525841575280...
%e A004790 11 | 59875 | 11.0000143347132163589...
%e A004790 12 | 162755 = a(10) | 12.0000012815651115743...
%e A004790 13 | 442414 | 13.0000013742591718739...
%e A004790 14 | 1202605 = a(11) | 14.0000005952373691014...
%e A004790 15 | 3269018 = a(12) | 15.0000001919622191103...
%e A004790 16 | 8886111 = a(13) | 16.0000000539597288735...
%e A004790 17 | 24154953 = a(14) | 17.0000000102018291255...
%e A004790 18 | 65659970 | 18.0000000131384387554...
%e A004790 19 | 178482301 = a(15) | 19.0000000002062542837...
%e A004790 20 | 485165196 | 20.0000000012165129058...
%e A004790 21 | 1318815735 | 21.0000000003918555785...
%e A004790 22 | 3584912847 | 22.0000000002422397629...
%e A004790 23 | 9744803447 = a(16) | 23.0000000000770767110...
%e A004790 24 | 26489122130 = a(17) | 24.0000000000059091314...
%e A004790 25 | 72004899338 | 25.0000000000085289679...
%e A004790 26 | 195729609429 = a(18) | 26.0000000000008237677...
%e A004790 27 | 532048240602 = a(19) | 27.0000000000003785057...
%e A004790 28 | 1446257064292 = a(20) | 28.0000000000003628859...
%e A004790 29 | 3931334297145 = a(21) | 29.0000000000002436642...
%e A004790 30 | 10686474581525 = a(22) | 30.0000000000000503302...
%e A004790 31 | 29048849665248 = a(23) | 31.0000000000000197862...
%e A004790 32 | 78962960182681 = a(24) | 32.0000000000000038605...
%e A004790 33 | 214643579785917 | 33.0000000000000043578...
%e A004790 34 | 583461742527455 = a(25) | 34.0000000000000002032...
%e A004790 35 | 1586013452313431 = a(26) | 35.0000000000000001714...
%e A004790 36 | 4311231547115196 | 36.0000000000000001792...
%e A004790 .
%e A004790 For k = ceiling(e^m) > 2, 0 < frac(log(k)) < e^(-m), so frac(log(k)) must approach 0 as m increases, but it does not do so monotonically; at values of m where frac(log(k)) is particularly small relative to e^(-m) (e.g., at m = 8 or m = 19), the next term after a(n) = k = ceiling(e^m) can be as large as a(n+1) = ceiling(e^(ceiling(-log(frac(log(k)))))).
%e A004790 (End)
%o A004790 (PARI) lista(n) = {last = frac(log(2));for (k=2, n, new = frac(log(k)); if (new < last, print1 (k, ", "); last = new;););} \\ _Michel Marcus_, Mar 21 2013
%Y A004790 Cf. A004791.
%K A004790 nonn
%O A004790 1,1
%A A004790 _Clark Kimberling_
%E A004790 More terms from _David W. Wilson_
%E A004790 a(24)-a(26) from _Jon E. Schoenfield_, May 28 2018