A216052 The sum of the primes less than or equal to n minus the sum of the distinct elements of the Goldbach partitions of n.

0, 2, 5, 3, 5, 7, 10, 9, 8, 2, 28, 16, 28, 20, 26, 9, 58, 22, 58, 37, 56, 22, 100, 28, 75, 35, 100, 44, 129, 39, 129, 96, 127, 41, 160, 16, 197, 140, 158, 77, 238, 70, 238, 149, 236, 120, 328, 88, 279, 128, 328, 172, 381, 111, 326, 213, 381, 178, 440, 80, 440

Offset

1,2

Comments

If n is prime then a(n) sets or equals a record.

If n and n+2 are twin primes then a(n) = a(n+2).

Links

J. Stauduhar, Table of n, a(n) for n = 1..10000

Example

With n = 2, the sum of the primes <= 2 is 2, and the sum of the distinct elements of the Goldbach partitions of 2 is 0, so a(2) = 2 + 0 = 2.
With n = 4, the sum of the primes <= 4 is 5, and the sum of the distinct elements of the Goldbach partitions of is 2, so a(4) = 5 - 2 = 3.

Mathematica

f[n_] := Module[{lst={}}, For[i=1, i<=n, i++, t = Plus @@ Select[ Table[Prime[i], {i, PrimePi[i]}], !PrimeQ[i-#]&]; AppendTo[lst, t]]; lst]; f[1000] (* J. Stauduhar, Sep 22 2012 *)

Crossrefs

Sequence in context: A078376 A226123 A368658 * A021911 A248852 A299210

Adjacent sequences: A216049 A216050 A216051 * A216053 A216054 A216055

Keyword

nonn

Author

J. Stauduhar, Sep 22 2012

Status

approved