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

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 *)

Crossrefs

Cf. A001221, A014574, A078571, A078572.

Sequence in context: A181611 A064740 A080967 * A295284 A292995 A037179

Adjacent sequences: A078567 A078568 A078569 * A078571 A078572 A078573

Keyword

nonn

Author

Reinhard Zumkeller, Nov 29 2002

Status

approved