

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 n1 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]] (* JeanFrançois 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 JeanFrançois Alcover, Jan 20 2018


STATUS

approved



