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A214196 Primes of the "first kind". 2

%I

%S 2,3,5,11,23,29,37,41,47,73,131,151,199,223,271,281,353,457,641,643,

%T 659,1259,1531,1747,1951,2671,2953,4259,4967,5419,5839,7013,7963,11261

%N Primes of the "first 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 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

%H Z.-W. Sun, <a href="http://arxiv.org/abs/1202.6589">On functions taking only prime values</a>, arXiv preprint arXiv:1202.6589 [math.NT], 2012; see p. 5.

%p A214196 := proc(n)

%p local m ,i,j,ddvs;

%p for m from 2 do

%p ddvs := false ;

%p for i from 1 to n-1 do

%p for j from i+1 to n do

%p if (A002110(j)-A002110(i)) mod m = 0 then

%p ddvs := true;

%p break;

%p end if;

%p end do:

%p if ddvs then

%p break;

%p end if;

%p end do:

%p if ddvs = false then

%p return m;

%p end if;

%p end do:

%p end proc:

%p # loop generates m multiples times (pipe through 'uniq')

%p for n from 1 do

%p printf("%d,\n",A214196(n)) ;

%p end do: # _R. J. Mathar_, Jul 08 2012

%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 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-Fran├žois Alcover_, Jan 20 2018, after _R. J. Mathar_ *)

%Y Cf. A214197.

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_, Jul 07 2012

%E a(28)-a(34) from _Jean-Fran├žois Alcover_, Jan 20 2018

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Last modified January 22 04:27 EST 2020. Contains 331133 sequences. (Running on oeis4.)