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 A002091 M2773 N1116 #43 Oct 14 2023 21:15:13
%S A002091 3,9,19,21,55,115,193,323,611,1081,1571,10771,13067,16321,44881,57887,
%T A002091 93167,189947,404939,442307,1746551,3383593,3544391,5056787,7480667,
%U A002091 25619213,87170987,404940757,526805663,707095391,1009465507,1048720723,5315914139
%N A002091 From a Goldbach conjecture: the location of records in A185091.
%C A002091 A stronger version of the second Goldbach conjecture (every odd number can be expressed as the sum of 3 primes) states that every odd number k > 5 can be written as k = 2*p + q, p, q prime. The conjecture was posed by E. Lemoine and later by H. Levy. The article by B. H. Mayoh assumes q {1,prime}. For the representations of k minimizing q, the sequence gives the value of k at which a larger q than for all representations of j < k is required. The new record value of q is given in A002092. The corresponding sequences for q prime and q=1 excluded are A194828 and A194829. - _Hugo Pfoertner_, Sep 03 2011
%C A002091 k is in this list when (k+1)/2 is the index of a record in A185091.
%C A002091 Checked up to k=10^13. a(50) is > 10^13. - _Hugo Pfoertner_, Sep 25 2011
%D A002091 Brian H. Mayoh, On the second Goldbach conjecture, Nordisk Tidskr. Informations-Behandling 6, 1966, 48-50.
%D A002091 Emile Lemoine, L'intermédiaire des mathématiciens, 1 (1894), 179; ibid 3 (1896), 151.
%D A002091 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002091 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002091 Hugo Pfoertner, <a href="/A002091/b002091.txt">Table of n, a(n) for n = 1..49</a>
%H A002091 Brian H. Mayoh, <a href="http://www.springerlink.com/content/v8p0525xw284234t/">On the second Goldbach conjecture</a>, BIT Numerical Mathematics 6 (1966) 1, 48-50
%H A002091 Wikipedia, <a href="http://en.wikipedia.org/wiki/Lemoine%27s_conjecture">Lemoine's conjecture</a>
%H A002091 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%e A002091 a(3)=19, because it is the first number for which q=5 is required. 3=2*1+1, 5=2*2+1, 7=2*3+1, 9=2*3+3, 11=2*5+1, 13=2*5+3, 15=2*7+1, 17=2*7+3, 19=2*7+5.
%Y A002091 Cf. A002092 [values of q], A194828, A194829 [equivalent with q=1 excluded].
%Y A002091 Cf. A185091.
%K A002091 nonn
%O A002091 1,1
%A A002091 _N. J. A. Sloane_
%E A002091 a(19)-a(32) from _Hugo Pfoertner_, Sep 03 2011
%E A002091 a(33) from Jason Kimberley, a(34)-a(40) from _Hugo Pfoertner_, Sep 09 2011
%E A002091 a(41)-a(49) from _Hugo Pfoertner_, Sep 25 2011