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

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, 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, 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

Offset: 1

Author

Reinhard Zumkeller, Nov 29 2002

Keywords

• nonn

Examples

			10th twin prime pair = (A001359(10), A006512(10)) = (107,109), hence A014574(10) = 108 = 2^2 * 3^2, therefore a(10) = 2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359, A006512, A014574, A051904, A078571, A078573.

Programs

Maple

p:= 2: count:= 0: Res:= NULL:
while count < 100 do
  q:= nextprime(p);
  if q - p = 2 then
    count:= count+1;
    Res:= Res, min(map(t->t[2],ifactors(p+1)[2]))
  fi;
  p:= q;
od:
Res; # Robert Israel, Oct 26 2018

Mathematica

Min[Transpose[FactorInteger[Mean[#]]][[2]]]&/@Select[Partition[Prime[ Range[ 1000]],2,1], #[[2]]-#[[1]]==2&] (* Harvey P. Dale, Mar 04 2013 *)

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

Formula

a(n) = A051904(A014574(n)).