A251364 Difference between average of two consecutive odd primes and the sum of all prime factors of the average.

0, 1, 3, 5, 7, 10, 11, 11, 20, 15, 23, 30, 34, 38, 43, 48, 52, 43, 60, 53, 69, 41, 59, 82, 80, 90, 95, 71, 106, 83, 65, 110, 130, 135, 134, 145, 146, 146, 157, 165, 150, 177, 174, 179, 159, 179, 209, 202, 210, 173, 224, 200, 125, 238, 238, 254

Offset

1,3

Comments

Sequence starts with the 2nd prime because the average of the first two primes is not an integer.

Links

Conner L. Delahanty, Table of n, a(n) for n = 1..20000

Formula

a(n) = ((prime(n+1) + prime(n+2))/2) - (sopfr((prime(n+1) + prime(n+2))/2)), where sopfr is A001414, the sum of primes dividing n (with repetition).

Example

For n = 1, the average of prime(2) and prime(3) is 4. The prime factors of 4 are 2 and 2. 4 - (2 + 2) = 0.
For n = 2, the average of prime(3) and prime(4) is 6. The prime factors of 6 are 2 and 3. 6 - (2 + 3) = 1.
For n = 3, the average of prime(4) and prime(5) is 9. The prime factors of 9 are 3 and 3. 9 - (3 + 3) = 3.
For n = 4, the average of prime(5) and prime(6) is 12. The prime factors of 12 are 2, 2, and 3. 12 - (2 + 2 + 3) = 5.

Mathematica

f[{a_, b_}] := Table[a, {b}]; g[n_] := Block[{d = (Prime[n + 1] + Prime[n])/2}, d - Plus @@ Flatten[f /@ FactorInteger@ d]]; Table[g@ n, {n, 2, 57}] (* Michael De Vlieger, Mar 25 2015 *)

Crossrefs

Cf. A000040 (primes), A001414 (sopfr).

Sequence in context: A319585 A133452 A356665 * A229791 A189293 A140607

Adjacent sequences: A251361 A251362 A251363 * A251365 A251366 A251367

Keyword

nonn,easy

Author

Conner L. Delahanty, Mar 20 2015

Status

approved