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

1,1

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

Table of n, a(n) for n=1..37.

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

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 *)

Crossrefs

Cf. A214196.

Sequence in context: A332216 A059878 A105017 * A083771 A158069 A039726

Adjacent sequences: A214194 A214195 A214196 * A214198 A214199 A214200

Keyword

nonn,more

Author

N. J. A. Sloane, Jul 07 2012

Extensions

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

Status

approved