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A078572
The minimum exponent in prime factorization of the average of n-th twin prime pair.
4
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 29 2002
STATUS
approved