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A078572 Minimal 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

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

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 *)

CROSSREFS

Cf. A078571, A078573.

Sequence in context: A195007 A276947 A178085 * A122750 A329041 A238744

Adjacent sequences:  A078569 A078570 A078571 * A078573 A078574 A078575

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Nov 29 2002

STATUS

approved

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Last modified January 23 03:15 EST 2022. Contains 350504 sequences. (Running on oeis4.)