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A214096 Smallest m such that prime(i) + prime(i-1) < prime(2*i-n) for all i>=m.

%I A214096 #17 Nov 27 2018 16:16:50
%S A214096 3,4,7,8,18,19,27,28,36,39,50,50,53,70,71,72,77,85,105,105,106,108,
%T A214096 110,111,114,143,144,144,149,149,153,161,165,172,173,173,226,228,228,
%U A214096 229,231,232,236,237,238,245,245,246,248,300,300,301,302,303,315,315
%N A214096 Smallest m such that prime(i) + prime(i-1) < prime(2*i-n) for all i>=m.
%C A214096 Formula given in Deléglise and Nicolas, Lemma 2.4, p.6. A002809 and A159685 are given explicitly on p.2.  Additional values given: a(3675) = 33127.
%H A214096 Jean-François Alcover, <a href="/A214096/b214096.txt">Table of n, a(n) for n = 1..3675</a>
%H A214096 Marc Deléglise, Jean-Louis Nicolas, <a href="http://arxiv.org/abs/1207.0603">Maximal product of primes whose sum is bounded</a>, arXiv:1207.0603v1 [math.NT], June 3, 2012.
%F A214096 a(n) is minimal such that prime(i) + prime(i-1) < prime(2*i-n) for i >= a(n).
%t A214096 a[1] = 3;
%t A214096 a[n_] := a[n] = Module[{}, For[m = a[n-1], True, m++, If[AllTrue[Range[m, 2 m], Prime[#] + Prime[# - 1] < Prime[2# - n]&], Return[m]]]];
%t A214096 Table[Print[n, " ", a[n]]; a[n], {n, 1, 100}] (* _Jean-François Alcover_, Nov 27 2018 *)
%Y A214096 Cf. A000040, A002809, A159685.
%K A214096 nonn
%O A214096 1,1
%A A214096 _Jonathan Vos Post_, Jul 04 2012
%E A214096 More terms from _Alois P. Heinz_, Jul 07 2012