cp's OEIS Frontend

A078572 The minimum exponent in prime factorization of the average of n-th twin prime pair.

%I A078572 #19 Sep 09 2024 02:41:00
%S A078572 2,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,1,1,1,3,1,1,1,1,1,1,1,1,1,1,1,
%T A078572 1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A078572 1,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1
%N A078572 The minimum exponent in prime factorization of the average of n-th twin prime pair.
%H A078572 Robert Israel, <a href="/A078572/b078572.txt">Table of n, a(n) for n = 1..10000</a>
%F A078572 a(n) = A051904(A014574(n)).
%e A078572 10th twin prime pair = (A001359(10), A006512(10)) = (107,109), hence A014574(10) = 108 = 2^2 * 3^2, therefore a(10) = 2.
%p A078572 p:= 2: count:= 0: Res:= NULL:
%p A078572 while count < 100 do
%p A078572   q:= nextprime(p);
%p A078572   if q - p = 2 then
%p A078572     count:= count+1;
%p A078572     Res:= Res, min(map(t->t[2],ifactors(p+1)[2]))
%p A078572   fi;
%p A078572   p:= q;
%p A078572 od:
%p A078572 Res; # _Robert Israel_, Oct 26 2018
%t A078572 Min[Transpose[FactorInteger[Mean[#]]][[2]]]&/@Select[Partition[Prime[ Range[ 1000]],2,1], #[[2]]-#[[1]]==2&] (* _Harvey P. Dale_, Mar 04 2013 *)
%o A078572 (PARI) lista(pmax) = {my(prv = 2); forprime(p = 3, pmax, if(p - prv ==2, print1(vecmin(factor(p-1)[,2]), ", ")); prv = p);} \\ _Amiram Eldar_, Sep 08 2024
%Y A078572 Cf. A001359, A006512, A014574, A051904, A078571, A078573.
%K A078572 nonn
%O A078572 1,1
%A A078572 _Reinhard Zumkeller_, Nov 29 2002