A214197 Primes of the "second kind".

2, 3, 5, 7, 11, 19, 23, 47, 59, 61, 71, 101, 113, 223, 487, 661, 719, 811, 947, 1327, 1621, 2039, 2161, 2377, 2381, 2699, 2957, 3011, 3607, 3727, 4093, 4549, 4649, 5939, 6473, 8363, 9601

Offset: 1

Author

N. J. A. Sloane, Jul 07 2012

Keywords

• nonn
• more

Comments

See Sun 2012 for precise definition. This term is overworked, and it would be good to include a more precise definition here.

Difference with A214196: sum of "primorial" products (A002110) is used here instead of difference. - Jean-François Alcover, Jan 20 2018

Links

• Zhi-Wei Sun, On functions taking only prime values, arXiv preprint arXiv:1202.6589, 2012; see p. 5.

Crossrefs

Cf. A214196.

Programs

Mathematica

primorial[n_] := primorial[n] = Product[Prime[i], {i, 1, n}];
p[0] = 1; p[n_] := p[n] = Module[{m, i, j, ddvs}, For[m = 2, True, m++, ddvs = False; For[i = 1, i <= n - 1, i++, For[j = i + 1, j <= n, j++, If[Mod[primorial[j] + primorial[i], m] == 0, ddvs = True; Break[]]]; If[ddvs, Break[]]]; If[ddvs == False, Return[m]]]];
A214197 = Reap[n = k = 1; While[n <= 400, If[p[n] != p[n - 1], a[k] = p[n]; Print[n, " a(", k, ") = ", a[k]]; Sow[a[k]]; k++]; n++]][[2, 1]] (* Jean-François Alcover, Jan 20 2018, after R. J. Mathar *)

Extensions

a(21)-a(37) from Jean-François Alcover, Jan 20 2018