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

3, 4, 7, 8, 18, 19, 27, 28, 36, 39, 50, 50, 53, 70, 71, 72, 77, 85, 105, 105, 106, 108, 110, 111, 114, 143, 144, 144, 149, 149, 153, 161, 165, 172, 173, 173, 226, 228, 228, 229, 231, 232, 236, 237, 238, 245, 245, 246, 248, 300, 300, 301, 302, 303, 315, 315

Offset: 1

Author

Jonathan Vos Post, Jul 04 2012

Keywords

• nonn

Comments

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.

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..3675
• Marc Deléglise, Jean-Louis Nicolas, Maximal product of primes whose sum is bounded, arXiv:1207.0603v1 [math.NT], June 3, 2012.

Crossrefs

Cf. A000040, A002809, A159685.

Programs

Mathematica

a[1] = 3;
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]]]];
Table[Print[n, " ", a[n]]; a[n], {n, 1, 100}] (* Jean-François Alcover, Nov 27 2018 *)

Formula

a(n) is minimal such that prime(i) + prime(i-1) < prime(2*i-n) for i >= a(n).

Extensions

More terms from Alois P. Heinz, Jul 07 2012