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 A276498 #23 Jul 19 2017 21:33:06
%S A276498 1,3,5,7,10,13,16,19,22,25,29,32,36,39,43,47,51,54,58,62,66,71,75,79,
%T A276498 83,87,92,96,100,105,109,114,118,123,127,132,136,141,146,150,155,160,
%U A276498 165,169,174,179,184,189,194,199,203,208,213,218,223,228,233
%N A276498 Number of trials T of an event that occurs with probability 1-1/n that must be repeated consecutively so that the probability that the event occurs on all T trials (i.e., (1-1/n)^T) is minimally higher than 1/n.
%H A276498 Charles R Greathouse IV, <a href="/A276498/b276498.txt">Table of n, a(n) for n = 2..10000</a>
%F A276498 a(n) = round(log(1/n)/log(1-1/n)).
%F A276498 a(n) = n log n - (log n)/2 + O(1). - _Charles R Greathouse IV_, Sep 06 2016
%e A276498 a(20) = round(log(1/20)/log(1-1/20)) = round(log(0.05)/log(0.95)) = round(58.4...) = 58.
%e A276498 If a phenomenon P occurs with a 95% probability on any given trial, how many trials T must be performed so that the probability that P occurs on all T trials reduces to 5%? 0.95^T = 0.05 => T = log(0.05)/log(0.95) = 58.4... = 58 (rounded).
%t A276498 Table[Round[Log[1/n]/Log[1 - 1/n]], {n, 2, 58}] (* _Michael De Vlieger_, Sep 06 2016 *)
%o A276498 (PARI) a(n) = round (log(1/n)/log(1-1/n)); \\ _Michel Marcus_, Sep 05 2016
%o A276498 (PARI) a(n)=-log(n)\/log1p(-1/n) \\ _Charles R Greathouse IV_, Sep 05 2016
%K A276498 nonn
%O A276498 2,2
%A A276498 _Talha Ali_, Sep 05 2016
%E A276498 Name and Example edited by _Jon E. Schoenfield_, Jul 16 2017