A050808
Numbers k such that floor(exp(k)) is prime.
Original entry on oeis.org
1, 2, 18, 50, 127, 141, 267, 310, 2290, 4487, 5391, 14025
Offset: 1
- Eric Weisstein's World of Mathematics, e-Prime
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Do[ If[ PrimeQ[ Floor[ \[ExponentialE]^n] ], Print[n] ], {n, 0, 4750} ]
Select[Range[15000],PrimeQ[Floor[Exp[#]]]&] (* Harvey P. Dale, Oct 16 2012 *)
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is(n)=ispseudoprime(exp(n)\1) \\ Charles R Greathouse IV, Jan 03 2014
A050809
Primes of the form floor( exp(k) ).
Original entry on oeis.org
2, 7, 65659969, 5184705528587072464087, 14302079958348104463583671072905261080748384225250684971, 17199742630376622641833783925547830057256484050709158699244513
Offset: 1
a(3) = floor(e^18) = 65659969, which is prime.
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Select[Table[Floor[Exp[n]], {n, 150}], PrimeQ] (* Jayanta Basu, Jun 01 2013 *)
A004790
Numbers k >= 2 such that if 1 < j < k then (fractional part of log k) < (fractional part of log j).
Original entry on oeis.org
2, 3, 8, 21, 55, 149, 404, 1097, 2981, 162755, 1202605, 3269018, 8886111, 24154953, 178482301, 9744803447, 26489122130, 195729609429, 532048240602, 1446257064292, 3931334297145, 10686474581525, 29048849665248, 78962960182681, 583461742527455, 1586013452313431
Offset: 1
From _Jon E. Schoenfield_, May 28 2018: (Start)
k = ceiling(e^m) yields a term for some but not all positive integers m:
.
m | k=ceiling(e^m) | log(k)
---+---------------------------+--------------------------
1 | 3 = a(2) | 1.0986122886681096913...
2 | 8 = a(3) | 2.0794415416798359282...
3 | 21 = a(4) | 3.0445224377234229965...
4 | 55 = a(5) | 4.0073331852324709186...
5 | 149 = a(6) | 5.0039463059454591409...
6 | 404 = a(7) | 6.0014148779611500697...
7 | 1097 = a(8) | 7.0003344602752302459...
8 | 2981 = a(9) | 8.0000140936780714441...
9 | 8104 | 9.0001130459285193087...
10 | 22027 | 10.0000242525841575280...
11 | 59875 | 11.0000143347132163589...
12 | 162755 = a(10) | 12.0000012815651115743...
13 | 442414 | 13.0000013742591718739...
14 | 1202605 = a(11) | 14.0000005952373691014...
15 | 3269018 = a(12) | 15.0000001919622191103...
16 | 8886111 = a(13) | 16.0000000539597288735...
17 | 24154953 = a(14) | 17.0000000102018291255...
18 | 65659970 | 18.0000000131384387554...
19 | 178482301 = a(15) | 19.0000000002062542837...
20 | 485165196 | 20.0000000012165129058...
21 | 1318815735 | 21.0000000003918555785...
22 | 3584912847 | 22.0000000002422397629...
23 | 9744803447 = a(16) | 23.0000000000770767110...
24 | 26489122130 = a(17) | 24.0000000000059091314...
25 | 72004899338 | 25.0000000000085289679...
26 | 195729609429 = a(18) | 26.0000000000008237677...
27 | 532048240602 = a(19) | 27.0000000000003785057...
28 | 1446257064292 = a(20) | 28.0000000000003628859...
29 | 3931334297145 = a(21) | 29.0000000000002436642...
30 | 10686474581525 = a(22) | 30.0000000000000503302...
31 | 29048849665248 = a(23) | 31.0000000000000197862...
32 | 78962960182681 = a(24) | 32.0000000000000038605...
33 | 214643579785917 | 33.0000000000000043578...
34 | 583461742527455 = a(25) | 34.0000000000000002032...
35 | 1586013452313431 = a(26) | 35.0000000000000001714...
36 | 4311231547115196 | 36.0000000000000001792...
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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)))))).
(End)
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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
A079663
Sequence of the radicands that give the best radical approach to e.
Original entry on oeis.org
1, 2, 3, 6, 7, 19, 20, 148, 403, 1096, 1097, 2980, 2981, 8103, 59874, 162755, 1202603, 1202604, 3269017, 8886110, 8886111, 24154952, 24154953, 65659969, 178482301, 3584912846, 9744803446, 26489122130, 72004899337, 195729609428
Offset: 1
e-1^1 > e-2^1 > 3^1-e > e-6^(1/2) > e-7^(1/2) > e-19^(1/3) > e-20^(1/3) > ...
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ls = {}; mx = 1; Do[mn = Min[Abs[{n^(1/Floor[Log[n]]) - E, E - n^(1/Ceiling[Log[n]])}]]; If[mn < mx, mx = mn; AppendTo[ls, {n, mx}]], {n, 3, 500000}]; N[ls] // TableForm
Showing 1-4 of 4 results.
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