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

1,1

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A195007 A276947 A178085 * A122750 A329041 A238744

Adjacent sequences: A078569 A078570 A078571 * A078573 A078574 A078575

Keyword

nonn,changed

Author

Reinhard Zumkeller, Nov 29 2002

Status

approved