

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.


1



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
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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



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



KEYWORD

nonn


AUTHOR



STATUS

approved



