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 A295262 #17 Feb 22 2022 09:54:29
%S A295262 2,3,5,7,13,23,43,83,163,317,631,1259,2503,4001
%N A295262 Primes for "Landau's trick" to prove Bertrand's postulate for n < 4000.
%C A295262 Chapter 2 in the Aigner and Ziegler book is devoted to Bertrand's postulate. The proof given starts by showing Bertrand's postulate is true just for n < 4000.
%C A295262 After 2, each prime is less than twice the previous prime. So, even if these were the only primes up to 4002, Bertrand's postulate would still be true for the specified range.
%C A295262 However, these are different from the Bertrand primes (A006992) after 2503, as that sequence requires the very largest prime smaller than twice the previous one, since twice 2503 is 5006 and 5003 is the largest prime less than that.
%C A295262 Erdős Pál used this sequence, with 4001 instead of 5003, in his 1932 proof of Bertrand's postulate, attributing it to Edmund Landau ("einer Bemerkung des Herrn Landau"), which Aigner and Ziegler refer to as "Landau's trick" in their book.
%D A295262 Martin Aigner and Günter M. Ziegler, Proofs from the Book, Second Edition. Berlin (2001): Springer-Verlag, p. 7.
%H A295262 Erdos Pál, <a href="https://users.renyi.hu/~p_erdos/1932-01.pdf">Beweis eines Satzes von Tschebyshef</a>, Acta Sci. Math (Szeged) 5 (1930-1932), p. 198 (in German).
%Y A295262 Cf. A006992.
%K A295262 nonn,fini
%O A295262 1,1
%A A295262 _Alonso del Arte_, Nov 18 2017