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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

Table of n, a(n) for n=1..34.

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[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]]]];

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.)