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A078573
The maximum exponent in prime factorization of the average of n-th twin prime pair.
2
2, 1, 2, 2, 1, 1, 2, 3, 1, 3, 1, 2, 2, 6, 2, 2, 4, 3, 1, 3, 2, 2, 4, 1, 2, 1, 3, 1, 1, 2, 4, 1, 2, 1, 2, 2, 3, 2, 2, 2, 7, 1, 2, 1, 1, 3, 2, 2, 1, 4, 3, 4, 2, 1, 1, 2, 4, 1, 2, 2, 3, 2, 1, 3, 6, 1, 2, 1, 4, 1, 2, 1, 2, 5, 1, 7, 3, 1, 2, 1, 3, 3, 4, 5, 2, 2, 2, 2, 5, 2, 1, 1, 2, 3, 2, 1, 2, 3, 3, 2, 2, 1, 1, 1, 2
OFFSET
1,1
LINKS
FORMULA
a(n) = A051903(A014574(n)).
EXAMPLE
10th twin prime pair = (A001359(10), A006512(10)) = (107,109), hence A014574(10) = 108 = 2^2 * 3^2, therefore a(10) = 3.
MATHEMATICA
midQ[n_] := PrimeQ[n-1] && PrimeQ[n+1]; f[n_] := Max @@ FactorInteger[n][[;; , 2]]; f /@ Select[Range[5000], midQ] (* Amiram Eldar, Nov 03 2019 *)
Max[FactorInteger[Mean[#]][[All, 2]]]&/@Select[Partition[Prime[Range[1000]], 2, 1], #[[2]] - #[[1]]==2&] (* Harvey P. Dale, Apr 21 2022 *)
PROG
(PARI) lista(pmax) = {my(prv = 2); forprime(p = 3, pmax, if(p - prv ==2, print1(vecmax(factor(p-1)[, 2]), ", ")); prv = p); } \\ Amiram Eldar, Sep 09 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Nov 29 2002
STATUS
approved