The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A361089 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A361089

a(n) = smallest integer x such that Sum_{k = 2..x} 1/(k*log(log(k))) > n.
(history; published version)

#41 by OEIS Server at Sat Jul 15 05:33:51 EDT 2023

LINKS

Pascal Sebah, <a href="/A361089/b361089_1.txt">Table of n, a(n) for n = 2..35</a>

#40 by N. J. A. Sloane at Sat Jul 15 05:33:51 EDT 2023

STATUS

proposed

approved

Discussion

Sat Jul 15

05:33

OEIS Server: Installed first b-file as b361089.txt.

#39 by Artur Jasinski at Wed Jun 14 14:45:14 EDT 2023

STATUS

editing

proposed

#38 by Artur Jasinski at Wed Jun 14 14:45:07 EDT 2023

LINKS

Pascal Sebah, <a href="/A361089/b361089_1.txt">Table of n, a(n) for n = 2..35</a>

STATUS

proposed

editing

#37 by Artur Jasinski at Mon Jun 12 13:06:56 EDT 2023

STATUS

editing

proposed

#36 by Artur Jasinski at Mon Jun 12 13:06:26 EDT 2023

DATA

3, 5, 8, 21, 76, 389, 2679, 23969, 269777, 3717613, 61326301, 1188642478, 26651213526, 682263659097, 19720607003198, 637490095320513, 22857266906193924, 902495758030547840, 38993221443195969536, 183327372052233243852819720607003199, 637490095320530, 22857266906194526, 902495758030572213, 38993221443197045348, 1833273720522384358862

MATHEMATICA

(*slow procedure*)

(*quick procedure *)

aa = {3}; cons = 2.79776470352080492766050456553352884330850083202326989577856315;

Do[ww = w /. NSolve[LogIntegral[Log[w]] + cons == n, w];

AppendTo[aa, Round[ww][[1]]], {n, 3, 21}]; aa

STATUS

proposed

editing

#35 by Artur Jasinski at Sun Jun 11 16:45:13 EDT 2023

STATUS

editing

proposed

Discussion

Sun Jun 11

16:52

Artur Jasinski: @Jon I copied by mistake old version now should be OK?

16:57

Jon E. Schoenfield: ’Looks good to me! Thanks!

#34 by Artur Jasinski at Sun Jun 11 16:45:02 EDT 2023

EXAMPLE

a(2) = 3 because Sum_{k=2..3} 1/(xk*log(log(xk))) = 2.18008755... > 2 and Sum_{k=2..2} 1/(xk*log(log(xk))) = -1.364208386450... < 2.

a(7) = 389 because Sum_{k=2..389} 1/(xk*log(log(xk))) = 7.000345... > 7 and Sum_{k=2..388} 1/(xk*log(log(xk))) = 6.99890560988... < 7.

STATUS

proposed

editing

#33 by Artur Jasinski at Sun Jun 11 16:39:50 EDT 2023

STATUS

editing

proposed

Discussion

Sun Jun 11

16:43

Jon E. Schoenfield: Thanks. Are you sure about using “Sum_{2..3}” — with no variable identified inside the braces? I don’t recall having seen notation like that in the OEIS (or elsewhere).

#32 by Artur Jasinski at Sun Jun 11 16:39:11 EDT 2023

EXAMPLE

a(2) = 3 because Sum_{k = 2..3} 1/(kx*log(log(kx))) = 2.18008755... > 2 and Sum_{2..2} 1/(x*log(log(x))) = -1.364208386450... < 2.

a(7) = 389 because Sum_{k = 2..389} 1/(kx*log(log(kx))) = 7.000345... > 7 and Sum_{2..388} 1/(x*log(log(x))) = 6.99890560988... < 7.

STATUS

proposed

editing

Discussion

Sun Jun 11

16:39

Artur Jasinski: I hope that recent Example is that what You mean