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A214197 Primes of the "second kind". 2
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 (list; graph; refs; listen; history; text; internal format)
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: A228062 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

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Last modified January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)