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 A214196 Primes of the "first kind". 2
 2, 3, 5, 11, 23, 29, 37, 41, 47, 73, 131, 151, 199, 223, 271, 281, 353, 457, 641, 643, 659, 1259, 1531, 1747, 1951, 2671, 2953, 4259, 4967, 5419, 5839, 7013, 7963, 11261 (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. The sequence is the set of numbers m which are the minimum m for some triple 1 <= i < j <=k such that m divides none of the differences A002110(i)-A002110(j). - R. J. Mathar, Jul 08 2012 LINKS Z.-W. Sun, On functions taking only prime values, arXiv preprint arXiv:1202.6589 [math.NT], 2012; see p. 5. MAPLE A214196 := proc(n)         local m , i, j, ddvs;         for m from 2 do                 ddvs := false ;                 for i from 1 to n-1 do                         for j from i+1 to n do                                 if (A002110(j)-A002110(i)) mod m = 0 then                                         ddvs := true;                                         break;                                 end if;                         end do:                         if ddvs then                                 break;                         end if;                 end do:                 if ddvs = false then                         return m;                 end if;         end do: end proc: # loop generates m multiples times (pipe through 'uniq') for n from 1 do         printf("%d, \n", A214196(n)) ; end do: # R. J. Mathar, Jul 08 2012 MATHEMATICA primorial[n_] := primorial[n] = Product[Prime[i], {i, 1, n}]; p = 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]]]]; A214196 = 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. A214197. Sequence in context: A118333 A131101 A188534 * A246857 A005384 A118571 Adjacent sequences:  A214193 A214194 A214195 * A214197 A214198 A214199 KEYWORD nonn,more AUTHOR N. J. A. Sloane, Jul 07 2012 EXTENSIONS a(28)-a(34) from Jean-François Alcover, Jan 20 2018 STATUS approved

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Last modified December 5 10:45 EST 2019. Contains 329751 sequences. (Running on oeis4.)