A078570 - OEIS

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A078570

Number of distinct prime factors of the average of n-th twin prime pair.

1, 2, 2, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 4, 2, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 4, 3, 4, 3, 4, 3, 4, 2, 4, 3, 4, 4, 4, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 4, 4, 3, 3, 3, 3, 3, 4, 4, 3, 3, 5, 4, 3, 4, 2, 3, 3, 3, 5, 4, 3, 4, 3, 4, 3, 3, 3, 4, 4, 4, 3, 4, 3, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 4, 4, 4

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A001221(A014574(n)).

EXAMPLE

12th twin prime pair = (A001359(12), A006512(12)) = (149,151), hence A014574(12) = 150 = 2*3*5*5, therefore a(12) = 3.

MATHEMATICA

midQ[n_] := PrimeQ[n-1] && PrimeQ[n+1]; PrimeNu /@ Select[Range[5000], midQ] (* Amiram Eldar, Nov 03 2019 *)

PrimeNu[Mean[#]]&/@Select[Partition[Prime[Range[1000]], 2, 1], #[[2]]-#[[1]]==2&] (* Harvey P. Dale, Jul 31 2023 *)