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%I #11 Jan 20 2018 22:30:50
%S 2,3,5,7,11,19,23,47,59,61,71,101,113,223,487,661,719,811,947,1327,
%T 1621,2039,2161,2377,2381,2699,2957,3011,3607,3727,4093,4549,4649,
%U 5939,6473,8363,9601
%N Primes of the "second kind".
%C See Sun 2012 for precise definition. This term is overworked, and it would be good to include a more precise definition here.
%C Difference with A214196: sum of "primorial" products (A002110) is used here instead of difference. - _Jean-François Alcover_, Jan 20 2018
%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1202.6589">On functions taking only prime values</a>, arXiv preprint arXiv:1202.6589, 2012; see p. 5.
%t primorial[n_] := primorial[n] = Product[Prime[i], {i, 1, n}];
%t 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]]]];
%t 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_ *)
%Y Cf. A214196.
%K nonn,more
%O 1,1
%A _N. J. A. Sloane_, Jul 07 2012
%E a(21)-a(37) from _Jean-François Alcover_, Jan 20 2018
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